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- W14020220 abstract "In this dissertation we have mainly studied probabilistic properties of stochastic processes through its characteristic function.The first part proves that the log--spot in the Heston model has a infinitely smooth density and gives an expression of this density as an infinite convolution of Bessel type densities. Such properties are deduced from a factorization of the characteristic function, mainly obtained through an analysis of the complex moment generating function.The second part proves that certain quotients of entire functions are characteristic functions. Under some conditions, the probability law corresponding to a characteristic function of that type has a density which can be expressed as a generalized Dirichlet series, whose coefficients are given in terms of the involved entire functions. As particular cases, conditions for the convergence of an infinite convolution of exponential or Laplace laws are deduced. This studies provide non trivial examples of meromorphic Levy processes.Finally, multiple integrals with respect to continuous centered Gaussian processes are considered to generalize the Levy area. We showed that under certain condition on the finite variation of their covariance functions, the Levy area can be defined as a double Wiener--Ito integral with respect to an isonormal Gaussian process. Moreover, some properties of the characteristic function of that generalized Levy area are studied." @default.
- W14020220 created "2016-06-24" @default.
- W14020220 creator A5008082017 @default.
- W14020220 date "2011-01-01" @default.
- W14020220 modified "2023-09-27" @default.
- W14020220 title "Stochastic calculus and analytic characteristic functions: applications to finance" @default.
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- W14020220 hasPublicationYear "2011" @default.
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