Matches in SemOpenAlex for { <https://semopenalex.org/work/W4211247320> ?p ?o ?g. }
- W4211247320 endingPage "189" @default.
- W4211247320 startingPage "177" @default.
- W4211247320 abstract "Free Access References Anatoliy Pogorui, Anatoliy PogoruiSearch for more papers by this authorAnatoliy Swishchuk, Anatoliy SwishchukSearch for more papers by this authorRamón M. Rodríguez-Dagnino, Ramón M. Rodríguez-DagninoSearch for more papers by this author Book Author(s):Anatoliy Pogorui, Anatoliy PogoruiSearch for more papers by this authorAnatoliy Swishchuk, Anatoliy SwishchukSearch for more papers by this authorRamón M. Rodríguez-Dagnino, Ramón M. Rodríguez-DagninoSearch for more papers by this author First published: 15 January 2021 https://doi.org/10.1002/9781119808152.refs AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat References Albeverio, S., Korolyuk, V., Samoilenko, I. (2009). Asymptotic expansion of semi-Markov random evolutions. Stochastics, 81(5), 477– 502. CrossrefGoogle Scholar Angell, J.S. and Olmstead, W.E. (1987). Singularly perturbed Volterra integral equations. SIAM Journal on Applied Mathematics, 47(1), 1– 14. CrossrefWeb of Science®Google Scholar Anisimov, V.V. (1977). Switched processes. Kibernetika, 4, 111– 115. Google Scholar Arfken, G., Weber, H.J., Harris, F.E. (2012). Mathematical Methods for Physicists, 7th edition. Academic Press, Cambridge. Google Scholar Arratia, R.A. (1979). Coalescing Brownian motions on the line. PhD Thesis, University of Wisconsin, Madison. Google Scholar Avellaneda, M., Levy, A., Paras, A. (1995). Pricing and hedging derivative securities in markets with uncertain volatility. Applied Mathematical Finance, 2, 73– 88. CrossrefGoogle Scholar Balakrishnan, V., Van den Broeck, C., Hänggi, P. (1988). First-passage of non-Markovian processes: The case of a reflecting boundary. Physical Review A, 38(8), 4213– 4222. CrossrefCASWeb of Science®Google Scholar Banchoff, T. (1976). Self linking numbers of space polygons. Indiana University Mathematics Journal, 25(12), 1171– 1188. CrossrefWeb of Science®Google Scholar Bateman, H. (1955). Higher Transcendental Functions. McGraw-Hill, New York. Google Scholar Bateman, H. (1954). Tables of Integral Transforms. McGraw-Hill, New York. Google Scholar Beghin, L. and Orsingher, E. (2010a). Moving randomly amid scattered obstacles. Stochastics, 82, 201– 229. CrossrefGoogle Scholar Beghin, L. and Orsingher, E. (2010b). Poisson-type processes governed by fractional and higher-order recursive differential equations. Electronic Journal of Probability, 15, 684–709 [Online]. Available at: 10.1214/EJP.v15-762. CrossrefWeb of Science®Google Scholar Benth, F.E., Groth, M., Kufakunesu, R. (2007). Valuing volatility and variance swaps for a non-Gaussian Ornstein–Uhlenbeck stochastic volatility model. Applied Mathematical Finance, 14(4), 347– 363. CrossrefGoogle Scholar Bertoin, J. (2002). Self-attracting Poisson clouds in an expanding universe. Communications in Mathematical Physics, 232, 59– 81. CrossrefWeb of Science®Google Scholar Black, F. and Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81, 637– 54. CrossrefWeb of Science®Google Scholar Bochner, S. and Chandrasekhar, K. (1949). Fourier Transforms, Volume 19: Annals of Mathematics Studies. Princeton University Press, Princeton. Google Scholar Bollerslev, T. (1986). Generalized autoregressive conditional heteroscedasticity. Journal of Economics, 31, 307– 327. CrossrefWeb of Science®Google Scholar Bossu, S. (2005). Arbitrage pricing of equity correlation swaps. Working paper, J.P. Morgan Equity Derivatives, London. Google Scholar Bossu, S. (2007). A new approach for modelling and pricing correlation swaps. Equity Structuring. Working paper, ECD, London. Google Scholar Broadie, M. and Jain, A. (2008a). The effect of jumps and discrete sampling on volatility and variance swaps. International Journal of Theoretical and Applied Finance, 11(8), 761– 797. CrossrefGoogle Scholar Broadie, M. and Jain, A. (2008b). Pricing and hedging volatility derivatives. The Journal of Derivatives, 15(3), 7– 24. CrossrefWeb of Science®Google Scholar Brockhaus, O. and Long, D. (2000). Volatility swap made simple. Risk, 2(1), 92– 96. Google Scholar Buff, R. (2002). Uncertain Volatility Model. Theory and Applications. Springer, New York. CrossrefGoogle Scholar Cahoy, D.O. (2007). Fractional Poisson process in terms of α-stable densities. PhD Thesis, Case Western University, Cleveland. Google Scholar Carr, P. and Lee, R. (2007). Realized volatility and variance: Options via swaps. Technical report, Bloomberg LP and University of Chicago [Online]. Available at: http://math.uchicago.edu/∼rl/OVSwithAppendices.pdf. Google Scholar Carr, P. and Lee, R. (2009). Volatility derivatives. Annual Review of Financial Economics, 1, 319– 39. CrossrefWeb of Science®Google Scholar Carr, P., Geman, H., Madan, D.B., Yor, M. (2005). Pricing options on realized variance. Finance and Stochastics, 9, 453– 475. CrossrefWeb of Science®Google Scholar Chesney, M. and Scott, L. (1989). Pricing European currency options: A comparison of modified Black–Scholes model and a random variance model. Journal of Financial and Quantitative Analysis, 24(3), 267– 284. CrossrefWeb of Science®Google Scholar Cox, D.R. (1970). Renewal Theory. Methuen & Co., London. Google Scholar Cox, J. and Ross, R. (1976). Valuation of options for alternative stochastic processes. Journal of Financial Economics, 3(1), 145– 166. CrossrefWeb of Science®Google Scholar Cox, J., Ross, S., Rubinstein, M. (1979). Option pricing: A simplified approach. Journal of Financial Economics, 7, 229– 263. CrossrefWeb of Science®Google Scholar Da Fonseca, J., Ielpo, F., Grasselli, M. (2009). Hedging (co)variance risk with variance swaps [Online]. Available at: http://ssrn.com/abstract=1341811. Google Scholar De Gregorio, A. (2012). On random flights with non-uniformly distributed directions. Journal of Statistical Physics, 147(2), 382– 411. CrossrefWeb of Science®Google Scholar De Gregorio, A. (2014). A family of random walks with generalized Dirichlet steps. Journal of Mathematical Physics, 55, 023302. CrossrefWeb of Science®Google Scholar De Gregorio, A. and Orsingher, E. (2012). Flying randomly in Rd with Dirichlet displacements. Stochastic Processes and their Applications, 122, 676– 713. CrossrefWeb of Science®Google Scholar De Gregorio, A., Orsingher, E., Sakhno, L. (2005). Motions with finite velocity analyzed with order statistics and differential equations. Theory of Probability and Mathematical Statistics, 71, 63– 79. CrossrefGoogle Scholar Demeterfi, K., Derman, E., Kamal, M., Zou, J. (1999). A guide to volatility and variance swaps. The Journal of Derivatives, 6(4), 9– 32. CrossrefGoogle Scholar Derman, E. (1999). Regimes of volatility. Risk, 4, 55– 59. Google Scholar Derman, E. and Kani, I. (1994). Riding on a smile. Risk, 7(2), 32– 39. Google Scholar Di Crescenzo, A. (2001). On random motions with velocities alternating at Erlang-distributed random times. Advances in Applied Probability, 33, 690– 701. CrossrefWeb of Science®Google Scholar Di Masi, G.B., Kabanov, Y.M., Runggaldier, W.J. (1994). Hedging of options on stock under mean-square criterion and Markov volatilities. Theory Probability and Its Applications, 39(1), 211– 222. Web of Science®Google Scholar Dorogovtsev, A.A. (2007a). Fourier-Wiener transforms of functionals on arratia flow. Ukrainian Mathematical Bulletin, 4(3), 333– 354. Google Scholar Dorogovtsev, A.A. (2007b). Measure-valued stochastic processes and flows. Institute of Mathematics NAS of Ukraine, Kyiv. Google Scholar Dorogovtsev, A.A. (2010). One Brownian stochastic flow. Theory of Stochastic Processes, 10, 21– 25. Google Scholar D'Ovidio, M., Orsingher, E., Toaldo, B. (2014). Fractional telegraph-type equations and hyperbolic Brownian motion. Statistics & Probability Letters, 89, 131– 137. CrossrefWeb of Science®Google Scholar Drissien, J., Maenhout, P.J., Vilkov, G. (2009). The price of correlation risk: Evidence from equity options. The Journal of Finance, 64(3), 1377– 1406. Wiley Online LibraryWeb of Science®Google Scholar Duan, J. (1995). The Garch option pricing model. Mathematical Finance, 5, 13– 32. Wiley Online LibraryGoogle Scholar Dupire, B. (1994). Pricing with a smile. Risk, 7(1), 18– 20. Google Scholar Economou, A. (2002). An alternative model for queueing systems with single arrivals, batch services and customer coalescence. Queueing Systems, 40, 407– 432. CrossrefWeb of Science®Google Scholar Elliott, R. and Swishchuk, A.V. (2007). Pricing options and variance swaps in Markov-modulated Brownian markets. In Hidden Markov Models in Finance, R. Mamon, R. Elliott (eds), Springer, New York. CrossrefGoogle Scholar Elliott, R.J., Siu, T.K., Chan, L. (2007a). Pricing options under a generalized Markov-modulated jump-diffusion model. Stochastic Analysis and Applications, 25, 821– 843. CrossrefWeb of Science®Google Scholar Elliott, R.J., Siu, T.K., Chan, L. (2007b). Pricing volatility swaps under Heston's stochastic volatility model with regime switching. Applied Mathematical Finance, 14(1), 41– 62. CrossrefGoogle Scholar Feller, W. (1968). An Introduction to Probability Theory and Its Applications, Volume 1, 3rd edition. John Wiley & Sons, New York. Google Scholar Feller, W. (1971). An Introduction to Probability Theory and Its Applications, Volume 2, 2nd edition. John Wiley & Sons, New York. Google Scholar Föllmer, H. and Schweizer, M. (1991). Hedging of contingent claims under incomplete information. In Applied Stochastic Analysis Volume 5, M.H.A. Davis, R.J. Elliott (eds). Gordon and Breach, London. Google Scholar Föllmer, H. and Sondermann, D. (1986). Hedging of non-redundant contingent claim. In Contributions to Mathematical Economics, W. Hilenbrandt, A. Mas-Colell (eds). North-Holland, Amsterdam. Google Scholar Franceschetti, M. (2007). When a random walk of fixed length can lead uniformly anywhere inside a hypersphere. Journal of Theoretical Probability, 20, 813– 823. Google Scholar Frey, R. (1997). Derivative asset analysis in models with level-dependent and stochastic volatility. CWI Quarterly, 10, 1– 34. Google Scholar Gakhov, F.D. and Cherskii, Y.I. (1978). Convolution Type Equations [in Russian]. Nauka. Moscow. Google Scholar Garra, R. and Orsingher, E. (2014). Random flights governed by Klein-Gordon-type partial differential equations. Stochastic Processes and their Applications, 124, 2171– 2187. CrossrefWeb of Science®Google Scholar Giraud, C. (2001). Clustering in a self-gravitating one-dimensional gas at zero temperature. Journal of Statistical Physics, 105, 585– 604. CrossrefWeb of Science®Google Scholar Giraud, C. (2005). Gravitational clustering and additive coalescence. Stochastic Processes and their Applications, 115, 1302– 1322. CrossrefWeb of Science®Google Scholar Girko, V.L. (1982). Limit theorems for products of random matrices with positive elements [in Russian]. Teor. Veroyatnost. i Primenen., 27, 777– 783. Google Scholar Goldstein, S. (1951). On diffusion by discontinuous movements and on the telegraph equation. The Quarterly Journal of Mechanics and Applied Mathematics, 4, 129– 156. CrossrefWeb of Science®Google Scholar Gorostiza, L.G. (1973). The central limit theorem for random motions of d-dimensional Euclidean space. The Annals of Probability, 1(4), 603– 612. CrossrefWeb of Science®Google Scholar Gorostiza, L.G. and Griego, R.J. (1979). Strong approximations of diffusion processes by transport processes. Kyoto Journal of Mathematics, 19(1), 91– 103. CrossrefGoogle Scholar Gradshteyn, I.S. and Ryzhik, I.M. (1980). Tables of Integrals, Sums, Series and Products. Academic Press, San Diego. Google Scholar Gray, S. (1996). Modeling the conditional distribution of interest rates as a regime-switching process. Journal of Financial Econometrics, 42, 27– 62. CrossrefWeb of Science®Google Scholar Griego, R. and Hersh, R. (1969). Random evolutions, Markov chains, and systems of partial differential equations. Proceedings of the National Academy of Sciences, 62, 305–308. Google Scholar Griego, R. and Hersh, R. (1971). Theory of random evolutions and applications to partial differential equations. Transactions of the American Mathematical Society, 156, 405– 418. CrossrefWeb of Science®Google Scholar Griego, R. and Korzeniowski, A. (1989). On principal eigenvalues for random evolutions. Stochastic Analysis and Applications, 7, 35– 45. CrossrefWeb of Science®Google Scholar Griego, R. and Swishchuk, A.V. (2000). Black-Scholes formula for a market in a Markov environment. Theory of Probability and Mathematical Statistics, 62, 9– 18. Google Scholar Hamilton, J. (1989). Rational-expectations econometric analysis of changes in regime. Journal of Economic Dynamics and Control, 12, 385– 423. CrossrefWeb of Science®Google Scholar Harrison, J. and Pliska, S. (1981). Martingales, stochastic integrals in the theory of continuous trading. Stochastic Processes and their Applications, 11(3), 215– 260. CrossrefWeb of Science®Google Scholar Hersh, R. (1974). Random evolutions: A survey of results and problems. Rocky Mountain Journal of Mathematics, 4, 443– 477. CrossrefGoogle Scholar Hersh, R. (2003). The birth of random evolutions. The Mathematical Intelligencer, 25(1), 53– 60. CrossrefWeb of Science®Google Scholar Hersh, R. and Papanicolaou, G. (1972). Non-commuting random evolutions, and an operator-valued Feynman–Kac formula. Communications on Pure and Applied Mathematics, 30, 337– 367. Wiley Online LibraryWeb of Science®Google Scholar Hersh, R. and Pinsky, M. (1972). Random evolutions are asymptotically Gaussian. Communications on Pure and Applied Mathematics, 25, 33– 44. Wiley Online LibraryWeb of Science®Google Scholar Heston, S. (1993). A closed-form solution for options with stochastic volatility with applications to bond and currency options. Review of Financial Studies, 6, 327– 343. CrossrefWeb of Science®Google Scholar Hobson, D. and Rogers, L. (1998). Complete models with stochastic volatility. Mathematical Finance, 8(1), 27– 48. Wiley Online LibraryWeb of Science®Google Scholar Howison, S., Rafailidis, A., Rasmussen, H. (2004). On the pricing and hedging of volatility derivatives. Applied Mathematical Finance, 11, 317– 346. CrossrefGoogle Scholar Hull, J. (2000). Options, Futures and Other Derivatives, 4th edition. Prentice Hall, Upper Saddle River. Google Scholar Hull, J. and White, A. (1987). The pricing of options on assets with stochastic volatilities. The Journal of Finance, 42, 281– 300. Wiley Online LibraryWeb of Science®Google Scholar Ignatovich, S.R., Kucher, A.G., Yakushenko, A.S., Bashta, A.V. (2004). Modeling of coalescence of dispersed surface cracks. Strength of Materials, 36(2), 125– 133. CrossrefGoogle Scholar Iksanov, A.M. and Rösler, U. (2006). Some moment results about the limit of a martingale related to the supercritical branching random walk and perpetuities. Ukrainian Mathematical Journal, 58(4), 451– 471. CrossrefGoogle Scholar Javaheri, A., Wilmott, P., Haug, E. (2002). Garch and volatility swaps. Technical article, WILMOTT. Google Scholar Johnson, H. and Shanno, D. (1987). Option pricing when the variance is changing. Journal of Financial and Quantitative Analysis, 22, 143– 151. CrossrefWeb of Science®Google Scholar Kac, M. (1974). A stochastic model related to the telegrapher's equation. Rocky Mountain Journal of Mathematics, 4, 497– 509. CrossrefGoogle Scholar Kazmerchuk, Y., Swishchuk, A.V., Wu, J. (2002). A continuous-time Garch model for stochastic volatility with delay. Canadian Applied Mathematics Quarterly, 13, 2. Google Scholar Kelvin, B. and Thomson, W. (1854). On the theory of the electric telegraph. Proceedings of the Royal Society of London, 7, 382–399. Google Scholar Kertz, R. (1978). Random evolutions with underlying semi-Markov processes. Publications of the Research Institute for Mathematical Sciences, 14(3), 589– 614. CrossrefGoogle Scholar Kolesnik, A.D. and Pinsky, M.A. (2011). Random evolutions are driven by the hyperparabolic operators. Journal of Statistical Physics, 142, 828– 846. CrossrefWeb of Science®Google Scholar Kolesnik, A. and Ratanov, N. (2013). Telegraph Processes and Option Pricing. Springer, Heidelberg. CrossrefGoogle Scholar Konarovskii, V.V. (2011). On infinite system of diffusing particles with coalescing. Theory of Probability and Its Applications, 55(1), 134– 144. CrossrefWeb of Science®Google Scholar Korn, G.A. and Korn, T.M. (2000). Mathematical Handbook for Scientists and Engineers, 2nd edition. Dover Publications, New York. Google Scholar Kornfeld, I.P., Sinai, Y.G., Fomin, S.V. (1982). Ergodic Theory. Springer-Verlag, Berlin. CrossrefGoogle Scholar Korolyuk, V.S. and Korolyuk, V.V. (1999). Stochastic Models of Systems. Kluwer Academic Publishers, Dordrecht. CrossrefWeb of Science®Google Scholar Korolyuk, V.S. and Limnios, N. (2004). Average and diffusion approximation for evolutionary systems in an asymptotic split phase space. The Annals of Applied Probability, 14(1), 489– 516. CrossrefWeb of Science®Google Scholar Korolyuk, V.S. and Limnios, N. (2005). Stochastic Systems in Merging Phase Space. World Scientific Publishing Company, New Jersey. CrossrefGoogle Scholar Korolyuk, V.S. and Limnios, N. (2009). Poisson approximation of processes with locally independent increments with Markov switching. Theory of Stochastic Processes, 15(1), 40– 48. Google Scholar Korolyuk, V.S. and Swishchuk, A.V. (1986). The central limit theorem for semi-Markov random evolutions. Ukrainian Mathematical Journal, 38, 286– 289. CrossrefGoogle Scholar Korolyuk, V.S. and Swishchuk, A.V. (1995). Semi-Markov Random Evolution. Kluwer Academic Publishers, Dordrecht. CrossrefGoogle Scholar Korolyuk, V.S. and Turbin, A.F. (1976). Semi-Markov Processes and their Applications. Naukova Dumka, Kyiv. Google Scholar Korolyuk, V.S. and Turbin, A.F. (1993). Mathematical Foundations of the State Lumping of Large Systems. Kluwer Academic Publishers, Dordrecht. CrossrefGoogle Scholar Kovalenko, I.N., Kuznetsov, N.Y., Shurenkov, V.M. (1983). Random Processes: Manual. Naukova Dumka, Kyiv. Google Scholar Krein, M.G. (1962). Integral equations on a half-line. In Nine papers on analysis, N.I. Ahiezer, I.A. Ăsnevic, Efimov, N.V., M.G. Kreĭn, N.A. Lebedev, A.I. Markŭsevĭc, A.B. Sidlovskiĭ, J.L. Šmul'jan, G.V. Ulina (eds). American Mathematical Society Translations: Series 2, Providence, Rhode Island. Google Scholar Lachal, A. (2006). Cyclic random motions in Rd -space with n directions. ESAIM: Probability and Statistics, 10, 277– 316. CrossrefGoogle Scholar Le, J.Y. and Raimond, O. (2004). Flows, coalescence and noise. The Annals of Probability, 32(2), 1247– 1315. CrossrefWeb of Science®Google Scholar Le Caër, G. (2010). A Pearson-Dirichlet random walk. Journal of Statistical Physics, 140, 728– 751. CrossrefWeb of Science®Google Scholar Le Caër, G. (2011). A new family of solvable Pearson-Dirichlet random walks. Journal of Statistical Physics, 144, 23– 45. CrossrefWeb of Science®Google Scholar Letac, G. and Piccioni, M. (2014). Dirichlet random walks. Journal of Applied Probability, 51, 1081– 1099. CrossrefWeb of Science®Google Scholar Lifshits, M. and Shi, Z. (2005). Aggregation rates in one-dimensional stochastic systems with adhesion and gravitation. The Annals of Probability, 33(1), 53– 81. CrossrefWeb of Science®Google Scholar López, O. and Ratanov, N. (2012). Option pricing under jump-telegraph model with random jumps. Journal of Applied Probability, 49(3), 838– 849. CrossrefWeb of Science®Google Scholar Marcus, A.H. (1968). Stochastic coalescence. Technometrics, 10(1), 133– 143. CrossrefWeb of Science®Google Scholar Masoliver, J., Porra, J.M., Weiss, G.H. (1993a). Solution to the telegrapher's equation in the presence of reflecting and partly reflecting boundaries. Physical Review, 48(2), 939– 944. CASGoogle Scholar Masoliver, J., Porrá, J.M., Weiss, G.H. (1993b). Some two and three-dimensional persistent random walks. Physica A, 193, 469– 482. CrossrefWeb of Science®Google Scholar Merton, R. (1973). Theory of rational option pricing. Bell Journal of Economic Management Science, 4, 141– 183. CrossrefWeb of Science®Google Scholar Meyer, P. (1969). Processus à accroissements indépendants et positifs. Séminaire de probabilitéss (Strasbourg), 3, 175– 189. Google Scholar Morse, P.M. and Feshbach, H. (1953). Methods of Theoretical Physics. McGraw-Hill, New York. Google Scholar Nischenko, I.I. (2001). On asymptotic representation normalizing multiplier for random matrix-valued evolution. Theory of Probability and Mathematical Statistics, 64, 129– 135. Google Scholar Orsingher, E. (1985). Hyperbolic equations arising in random models. Stochastic Processes and their Applications, 21, 93– 106. CrossrefWeb of Science®Google Scholar Orsingher, E. and Beghin, L. (2006). Probabiliti e modelli aleatori. Aracne, Rome. Google Scholar Orsingher, E. and Beghin, L. (2009). Fractional diffusion equations and processes with randomly-varying time. Annals of Probability, 37(1), 206– 249. CrossrefWeb of Science®Google Scholar Orsingher, E. and De Gregorio, A. (2007). Random flights in higher spaces. Journal of Theoretical Probability, 20, 769– 806. CrossrefWeb of Science®Google Scholar Orsingher, E. and Ratanov, N. (2002). Planar random motions with drift. Journal of Applied Mathematics and Stochastic Analysis, 15, 205– 221. CrossrefGoogle Scholar Orsingher, E. and Ratanov, N. (2007). Exact distributions of random motions in inhomogeneous media. Theory of Probability and Mathematical Statistics, 76, 125– 137. Google Scholar Orsingher, E. and Somella, A.M. (2004). A cyclic random motion in R3 with four directions and finite velocity. Stochastics and Stochastics Reports, 76, 113– 133. CrossrefGoogle Scholar Papanicolaou, G. (1971a). Asymptotic analysis of transport processes. Bulletin of the American Mathematical Society, 81, 330– 391. CrossrefWeb of Science®Google Scholar Papanicolaou, G. (1971b). Motion of a particle in a random field. Journal of Mathematical Physics, 12(24), 473– 489. Google Scholar Pilipenko, A.Y. (1999). The evolution of a system of particles and measure-valued processes. Theory of Stochastic Processes, 5(3–4), 188– 197. Google Scholar Pinsky, M. (1991). Lectures on Random Evolutions. World Scientific, Singapore. CrossrefGoogle Scholar Pogorui, A.A. (1989). Distribution of reaching time of infinitely increasing level by family of semi-Markov processes with extending phase space [in Russian]. In Analytical Methods of Research of Evolution Stochastic Systems, Institute of Mathematics of NAS of Ukraine, Kyiv. Google Scholar Pogorui, A.A. (1994). Asymptotic inequalities for the distribution of the time of stay of a semi-Markov process in an expanding set of states. Ukrainian Mathematical Journal, 46(11), 1757– 1762. CrossrefGoogle Scholar Pogorui, A.A. (2003). Estimation of the stationary efficiency of a two-phase system with two storages. Journal of Automation and Information Sciences, 35, 16– 23. CrossrefGoogle Scholar Pogorui, A.A. (2004). Estimation of the efficiency of a data transmission line with feedback. Journal of Automation and Information Sciences, 36, 44– 50. CrossrefGoogle Scholar Pogorui, A.A. (2005). Stationary distribution of the random shift process with delaying in reflecting boundaries. Scientific Journal of National Pedagogical Dragomanov University, Series 1, 6, 168– 172. Google Scholar Pogorui, A.A. (2006). Stationary distribution of a process of random semi-Markov evolution with delaying screens in the case of balance. Ukrainian Mathematical Journal, 58(3), 430– 437. CrossrefGoogle Scholar Pogorui, A.A. (2007). Hyperholomorphic functions in commutative algebras. Complex Variables and Elliptic Equations, 52(12), 1155– 1159. CrossrefGoogle Scholar Pogorui, A.A. (2009a). Asymptotic expansion for distribution of Markovian random motion. Random Operators and Stochastic Equations, 17(2), 189– 196. CrossrefGoogle Scholar Pogorui, A.A. (2009b). Stationary distributions of fading evolutions. Ukrainian Mathematical Journal, 61(3), 425– 431. Web of Science®Google Scholar Pogorui, A.A. (2010a). Asymptotic analysis for phase averaging of transport process. Ukrainian Mathematical Journal, 62(2), 190– 198. Web of Science®Google Scholar Pogorui, A.A. (2010b). Fading evolution in multidimensional spaces. Ukrainian Mathematical Journal, 62(11), 1577– 1582. Web of Science®Google Scholar Pogorui, A.A. (2011). The distribution of random evolution in Erlang semi-Markov media. Theory of Stochastic Processes, 17(33), 90– 99. Google Scholar Pogorui, A.A. (2012a). Evolution in multidimensional spaces. Random Operators and Stochastic Equations, 20(2), 135– 141. CrossrefGoogle Scholar Pogorui, A.A. (2012b). System of interactive particles with Markovian switching. Theory of Stochastic Processes, 18(34–2), 83– 95. Google Scholar Pogorui, A.A. and Rodríguez-Dagnino, R.M. (2005). One-dimensional semi-Markov evolution with general Erlang sojourn times. Random Operators and Stochastic Equations, 13(4), 399– 405. CrossrefGoogle Scholar Pogorui, A.A. and Rodríguez-Dagnino, R.M. (2006). Limiting distribution of random motion in an n-dimensional parallelepiped. Random Operators and Stochastic Equations, 14(4), 385– 392. CrossrefGoogle Scholar Pogorui, A.A. and Rodríguez-Dagnino, R.M. (2009a). Evolution process as an alternative to diffusion process and Black–Scholes formula. Random Operators and Stochastic Equations, 17(1), 61– 68. CrossrefGoogle Scholar Pogorui, A.A. and Rodríguez-Dagnino, R.M. (2009b). Limiting distribution of fading evolution in some semi-Markov media. Ukrainian Mathematical Journal, 61(12), 1720– 1724. CrossrefWeb of Science®Google Scholar Pogorui, A.A. and Rodríguez-Dagnino, R.M. (2010a). Asymptotic expansion for transport processes in semi-Markov media. Theory of Probability and Mathematical Statistics, 83, 127– 134. CrossrefGoogle Scholar Pogorui, A.A. and Rodríguez-Dagnino, R.M. (2010b). Stationary distribution of random motion with delay in reflecting boundaries. Applied Mathematics, 1(1), 24– 28. CrossrefGoogle Scholar Pogorui, A.A. and Rodríguez-Dagnino, R.M. (2011). Isotropic random motion at finite speed with k-Erlang distributed direction alternations. Journal of Statistical Physics, 145(1), 102– 112. CrossrefWeb of Science®Google Scholar Pogorui, A.A. and Rodríguez-Dagnino, R.M. (2012). Random motion with uniformly distributed directions and random velocity. Journal of Statistical Physics, 147(6), 1216– 1225. CrossrefWeb of Science®Google Scholar Pogorui, A.A. and Rodríguez-Dagnino, R.M. (2013). Random motion with gamma steps in higher dimensions. Statistics & Probability Letters, 83, 1638– 1643. CrossrefWeb of Science®Google Scholar Pogorui, A.A. and Turbin, A.F. (2002). Estimation of stationary efficiency of a production line with two unreliable aggregates. Cybernetics and Systems Analysis, 38, 823– 829. CrossrefGoogle Scholar Pogorui, A.A., Rodríguez-Dagnino, R.M., Shapiro, M. (2014). Solutions for PDEs with constant coefficients and derivability of functions ranged in commutative algebras. Mathematical Methods in the Applied Sciences, 37(17), 2799– 2810. Wiley Online LibraryWeb of Science®Google Scholar Prudnikov, A.P., Brychkov, Y., Marichev, O.I. (1986). Integrals and Series: More Special Functions. Gordon and Breach, London. Google Scholar Qian, H., Raymond, G.M., Bassingthwaighte, J.B. (1998). On two-dimensional fractional Brownian motion and fractional Brownian random field. Journal of Physics A: Mathematical and General, 31, 1527– 1535. CrossrefGoogle Scholar Ratanov, N. (2007). A jump telegraph model for option pricing. Quantitative Finance, 7(5), 575– 583. CrossrefWeb of Science®Google Scholar Ratanov, N. (2010). Option pricing model based on a Markov-modulated diffusion with jumps. The Brazilian Journal of Probability and Statistics, 24, 413– 431. CrossrefWeb of Science®Google Scholar Ratanov, N. and Melnikov, A. (2008). On financial markets based on telegraph processes. Stochastics, 80, 247– 268. CrossrefGoogle Scholar Rodríguez-Said, R.D., Pogorui, A.A., Rodríguez-Dagnino, R.M. (2007). Stationary probability distribution of a system with n equal customers with bursty demands connected to a single buffer. Random Operators and Stochastic Equations, 15(2), 181– 204. CrossrefGoogle Scholar Salvi, G. and Swishchuk, A.V. (2012a). Covariance and correlation swaps for financial markets with Markov-modulated volatility model. International Journal of Theoretical and Applied Finance, 17, 1. Google Scholar Salvi, G., Swishchuk, A.V. (2012b). Pricing of Variance, Volatility, Covariance and Correlation Swaps in a Markov-modulated Volatility Model. University of Calgary, Calgary. Google Scholar Samoilenko, I.V. (2001). Markovian random evolution in Rn . Random Operators and Stochastic Equations, 9, 247– 257. CrossrefGoogle Scholar Samoilenko, I.V. (2002). Fading Markov random evolution. Ukrainian Mathematical Journal, 54(3), 448– 459. CrossrefGoogle Scholar Samoilenko, I.V. (2005). Asymptotic expansion for the functional of Markovian evolution in Rd in the circuit of diffusion approximation. Journal of Applied Mathematics and Stochastic Analysis, 3, 247– 257. CrossrefGoogle Scholar Scott, L. (1987). Option pricing when the variance changes randomly: Theory, estimation and an application. Journal of Financial and Quantitative Analysis, 22, 419– 438. CrossrefWeb of Science®Google Scholar Sepp, A. (2008). Pricing options on realized variance in the Heston model with jumps in returns and volatility. Journal of Computational Finance, 11(4), 33– 70. CrossrefGoogle Scholar Shiryaev, A. (1999). Essentials of Stochastic Finance: Facts, Models, Theory. World Scientific, Singapore. CrossrefGoogle Scholar Shreve, S. (2004). Stochastic Calculus for Finance: Continuous-time Models. Springer, New York. Google Scholar Shubin, C. (2006). Singularly perturbed integral equations. Journal of Mathematical Analysis and Applications, 313(1), 234– 250. CrossrefWeb of Science®Google Scholar Shurenkov, V.M. (1986). Markov intervention of chance and limit theorems. Mathematics of the USSR-Sbornik, 54, 1. CrossrefGoogle Scholar Shurenkov, V.M. (1989). Ergodic Markov Processes [in Russian]. Nauka, Moscow. Google Scholar Sinai, Y.G. (1992). Distribution of some functionals of the integral of a random walk. Theoretical and Mathematical Physics, 90, 219– 241. CrossrefWeb of Science®Google Scholar Sinai, Y.G. (2010). Dynamical Systems, Ergodic Theory and Applications, Volume 100. Encyclopedia of Mathematical Sciences, Springer-Verlag, Berlin. Google Scholar Skorokhod, A.V. (1989). Asymptotic Methods in the Theory of Stochastic Differential Equations. American Mathematical Society, Rhode Island. Google Scholar Stadje, W. (2007). The exact probability distribution of a two-dimensional random walk. Journal of Statistical Physics, 56, 207– 216. Google Scholar Stadje, W. and Zacks, S. (2004). Telegraph processes with random velocities. Journal of Applied Probability, 41, 665– 678. CrossrefWeb of Science®Google Scholar Stein, E. and Stein, J. (1991). Stock price distributions with stochastic volatility: An analytic approach. The Review of Financial Studies, 4, 727– 752. CrossrefWeb of Science®Google Scholar Stroock, D.W. and Varadhan, S.R.S. (1969). Diffusion processes with continuous coefficients, Communications on Pure and Applied Mathematics, 22(3), 345– 400. Wiley Online LibraryWeb of Science®Google Scholar Stroock, D.W. and Varadhan, S.R.S. (1979). Multidimensional Diffusion Processes. Springer-Verlag, Berlin. Google Scholar Sviridenko, M.N. (1986). Martingale approach to limit theorems for semi-Markov processes. Theory of Probability and Its Applications, 540– 545. Google Scholar Swishchuk, A.V. (1989). Weak convergence of semi-Markov random evolutions in an averaging scheme (martingale approach). Ukrainian Mathematical Journal, 41(3), 1450– 1456. CrossrefGoogle Scholar Swishchuk, A.V. (1997). Hedging of options under mean-square criterion and with semi-Markov volatility. Ukrainian Mathematical Journal, 47(7), 1119– 1127. CrossrefGoogle Scholar Swishchuk, A.V. (2000). Random Evolutions and their Applications: New Trends. Kluwer Academic Publishers, Dordrecht. CrossrefGoogle Scholar Swishchuk, A.V. (2004). Modeling of variance and volatility swaps for financial markets with stochastic volatilities. WILMOTT Magazine, 2, 64– 72. Google Scholar Swishchuk, A.V. (2005). Modeling and pricing of variance swaps for stochastic volatilities with delay. WILMOTT Magazine, 19, 63– 73. Google Scholar Swishchuk, A.V. (2010). Pricing of variance and volatility swaps with semi-Markov volatilities. Canadian Applied Mathematics Quarterly, 18, 4. Google Scholar Swishchuk, A.V., Cheng, R., Lawi, S., Badescu, A., Mekki, H.B., Gashaw, A.F., Hua, Y., Molyboga, M., Neocleous, T., Petrachenko, Y. (2002). Price pseudo-variance, pseudo-covariance, pseudo-volatility, and pseudo-correlation swaps – In analytical closed-forms. In Proceedings of the Sixth PIMS Industrial Problems Solving Workshop, J. Macki (ed.). University of Alberta, Edmonton. Google Scholar Tautz, R.C. and Lerche, I. (2016). Application of the three-dimensional telegraph equation to cosmic-ray transport. Research in Astronomy and Astrophysics, 16, 10. CrossrefWeb of Science®Google Scholar Théoret, R., Zabré, L., Rostan, P. (2002). Pricing volatility swaps: Empirical testing with Canadian data. Working paper 17, Centre de Recherche en Gestion, Montreal. Google Scholar Tóth, B. and Werener, W. (1998). The true self-repelling motion. Probability Theory and Related Fields, 111, 375– 452. CrossrefWeb of Science®Google Scholar Turbin, A.F. (1972). The solution of some problems on perturbing the occurrence of matrices. Reports of the National Academy of Sciences of Ukraine Series A, 539– 541. Google Scholar Turbin, A.F. (1981). Limit theorems for perturbed semigroups and Markov processes in the scheme of asymptotic phase lumping [in Russian]. Institute of Mathematics, Ukrainian National Academy of Sciences, Preprint no. 80.18. 133– 147. Google Scholar Turbin, A.F. (1998). Mathematical models of one-dimensional Brownian motion as alternatives to the mathematical models of Einstein, Wiener, Levy [in Russian]. Fractal Analysis and Related Fields, 2, 47– 60. Google Scholar Vladimirov, V.S. (1996). Equations of Mathematical Physics. Mir Publishers, Moscow. Google Scholar Vysotsky, V.V. (2008a). Clustering in a stochastic model of one-dimensional gas. The Annals of Applied Probability, 18(3), 1026– 1058. CrossrefWeb of Science®Google Scholar Vysotsky, V.V. (2008b). Limit theorems for stochastic models of interacting particles. PhD Thesis, Saint Petersburg State University, Saint Petersburg. Google Scholar Watkins, J. (1984). A central limit theorem in random evolution. The Annals of Probability, 12(2), 480– 514. CrossrefWeb of Science®Google Scholar Watkins, J. (1985). Limit theorems for stationary random evolutions. Stochastic Processes and their Applications, 19, 189– 224. CrossrefWeb of Science®Google Scholar Wiggins, J. (1987). Option values under stochastic volatility: Theory and empirical estimates. Journal of Financial Economics, 19, 351– 372. CrossrefWeb of Science®Google Scholar Wilmott, P., Howison, S., Dewynne, J. (1995). Option Pricing: Mathematical Models and Computations. Oxford Financial Press, Oxford. Google Scholar Windcliff, H., Forsyth, P.A., Vetzal, K.R. (2006). Pricing methods and hedging strategies for volatility derivatives. Journal of Banking & Finance, 30, 409– 431. CrossrefWeb of Science®Google Scholar Yeleyko, Y.I. and Zhernovyi, Y.V. (2002). Asymptotic properties of stochastic evolutions described by the solutions of the ordinary differential equations partially solved with respect to the higher derivatives. Bulletin of the Lviv University, Series: Physics and Mathematics, 60, 60– 66. Google Scholar Random Motions in Markov and Semi‐Markov Random Environments 2: High‐dimensional Random Motions and Financial Applications ReferencesRelatedInformation" @default.
- W4211247320 created "2022-02-13" @default.
- W4211247320 date "2021-01-15" @default.
- W4211247320 modified "2023-09-23" @default.
- W4211247320 title "References" @default.
- W4211247320 cites W1508243775 @default.
- W4211247320 cites W1511098757 @default.
- W4211247320 cites W1540835690 @default.
- W4211247320 cites W1549524500 @default.
- W4211247320 cites W1582093212 @default.
- W4211247320 cites W159368019 @default.
- W4211247320 cites W1963875897 @default.
- W4211247320 cites W1964114385 @default.
- W4211247320 cites W1965658608 @default.
- W4211247320 cites W1966119267 @default.
- W4211247320 cites W1971765957 @default.
- W4211247320 cites W1972989640 @default.
- W4211247320 cites W1973012832 @default.
- W4211247320 cites W1973547983 @default.
- W4211247320 cites W1977201224 @default.
- W4211247320 cites W1979698494 @default.
- W4211247320 cites W1980849523 @default.
- W4211247320 cites W1981753607 @default.
- W4211247320 cites W1982759111 @default.
- W4211247320 cites W1984031927 @default.
- W4211247320 cites W1991604961 @default.
- W4211247320 cites W1991962858 @default.
- W4211247320 cites W1992007068 @default.
- W4211247320 cites W1993567429 @default.
- W4211247320 cites W1994997909 @default.
- W4211247320 cites W1995304448 @default.
- W4211247320 cites W1997293696 @default.
- W4211247320 cites W1997853375 @default.
- W4211247320 cites W1999996900 @default.
- W4211247320 cites W2009139510 @default.
- W4211247320 cites W2009558577 @default.
- W4211247320 cites W2011569659 @default.
- W4211247320 cites W2012058749 @default.
- W4211247320 cites W2012242451 @default.
- W4211247320 cites W2012930870 @default.
- W4211247320 cites W2013384370 @default.
- W4211247320 cites W2017297397 @default.
- W4211247320 cites W2020000885 @default.
- W4211247320 cites W2020055704 @default.
- W4211247320 cites W2022123904 @default.
- W4211247320 cites W2025006397 @default.
- W4211247320 cites W2027654260 @default.
- W4211247320 cites W2029448271 @default.
- W4211247320 cites W2030923857 @default.
- W4211247320 cites W2033341843 @default.
- W4211247320 cites W2034272815 @default.
- W4211247320 cites W2036442667 @default.
- W4211247320 cites W2040777649 @default.
- W4211247320 cites W2041550349 @default.
- W4211247320 cites W2044117621 @default.
- W4211247320 cites W2044965965 @default.
- W4211247320 cites W2049457585 @default.
- W4211247320 cites W2052596750 @default.
- W4211247320 cites W2052670680 @default.
- W4211247320 cites W2055980838 @default.
- W4211247320 cites W2058307814 @default.
- W4211247320 cites W2059353468 @default.
- W4211247320 cites W2061128599 @default.
- W4211247320 cites W2062108632 @default.
- W4211247320 cites W2064978316 @default.
- W4211247320 cites W2065983943 @default.
- W4211247320 cites W2068347317 @default.
- W4211247320 cites W2069618313 @default.
- W4211247320 cites W2071091278 @default.
- W4211247320 cites W2071355555 @default.
- W4211247320 cites W2072919545 @default.
- W4211247320 cites W2074753791 @default.
- W4211247320 cites W2077358099 @default.
- W4211247320 cites W2077791698 @default.
- W4211247320 cites W2078737002 @default.
- W4211247320 cites W2080452905 @default.
- W4211247320 cites W2081859301 @default.
- W4211247320 cites W2084206021 @default.
- W4211247320 cites W2094206697 @default.
- W4211247320 cites W2094495898 @default.
- W4211247320 cites W2098703547 @default.
- W4211247320 cites W2100534547 @default.
- W4211247320 cites W2105500720 @default.
- W4211247320 cites W2108367910 @default.
- W4211247320 cites W2109617541 @default.
- W4211247320 cites W2120022309 @default.
- W4211247320 cites W2120440418 @default.
- W4211247320 cites W2124022334 @default.
- W4211247320 cites W2143083943 @default.
- W4211247320 cites W2146207017 @default.
- W4211247320 cites W2146612430 @default.
- W4211247320 cites W2148080284 @default.
- W4211247320 cites W2149152656 @default.
- W4211247320 cites W2154085620 @default.
- W4211247320 cites W2157858527 @default.
- W4211247320 cites W2164399278 @default.
- W4211247320 cites W2169908486 @default.
- W4211247320 cites W2172288758 @default.