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• W2022761906 abstract "Next article The Distribution of the First Ladder Moment and Height and Fluctuation of a Random WalkB. A. RogozinB. A. Rogozinhttps://doi.org/10.1137/1116067PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Frank Spitzer, A combinatorial lemma and its application to probability theory, Trans. Amer. Math. Soc., 82 (1956), 323–339 MR0079851 0071.13003 CrossrefGoogle Scholar[2] E. B. Dynkin, Some limit theorems for sums of independent random quantities with infinite mathematical expectations, Izv. Akad. Nauk SSSR. Ser. Mat., 19 (1955), 247–266, (In Russian.) MR0076214 Google Scholar[3] William Feller, An introduction to probability theory and its applications. Vol. II, John Wiley & Sons Inc., New York, 1966xviii+636 MR0210154 0138.10207 Google Scholar[4] Ya. G. Sinai, On the distribution of the first positive sum for a sequence of independent random variables, Theory Prob. Applications, 2 (1957), 122–129 10.1137/1102009 LinkGoogle Scholar[5] William Feller, An introduction to probability theory and its applications. Vol. I, John Wiley and Sons, Inc., New York, 1957xv+461, 2nd ed. MR0088081 0077.12201 Google Scholar[6] E. A. Pecherskii and , B. A. Rogozin, On joint distributions of random variables associated with fluctuations of a process with independent increments, Theory Prob. Applications, 14 (1969), 410–423 10.1137/1114054 LinkGoogle Scholar[7] C. C. Heyde, Some local limit results in fluctuation theory, J. Austral. Math. Soc., 7 (1967), 455–464 MR0220335 0183.19903 CrossrefGoogle Scholar[8] G. M. Fikhtengol'ts, A Course in Differential and Integral Calculus, Vol. 2, Fizmatgiz, Moscow, 1959, (In Russian.) Google Scholar[9] I. A. Ibragimov and , Yu. V. Linnik, Independent and stationary sequences of random variables, Wolters-Noordhoff Publishing, Groningen, 1971, 443– MR0322926 0219.60027 Google Scholar[10] B. A. Rogozin, On the distribution of the first jump, Theory Prob. Applications, 9 (1964), 450–465 10.1137/1109060 LinkGoogle Scholar[11] Daniel Ray, Stable processes with an absorbing barrier, Trans. Amer. Math. Soc., 89 (1958), 16–24 MR0105178 0083.13804 CrossrefGoogle Scholar[12] B. A. Rogozin, On some classes of processes with independent increments, Theory Prob. Applications, 10 (1965), 479–483 10.1137/1110056 0161.37202 LinkGoogle Scholar[13] I. I. Gikhman and , A. V. Skorokhod, Introduction to the theory of random processes, Translated from the Russian by Scripta Technica, Inc, W. B. Saunders Co., Philadelphia, Pa., 1969xiii+516 MR0247660 Google Scholar[14] B. A. Rogozin, On distributions of functionals related to boundary problems for processes with independent increments, Theory Prob. Applications, 11 (1966), 580–591 10.1137/1111062 0178.52701 LinkGoogle Scholar[15] A. V. Skorokhod, Random Processes with Independent Increments, Izd-vo “Nauka”, Moscow, 1964, (In Russian.) Google Scholar[16] Michel Loève, Probability theory, 2nd ed. The University Series in Higher Mathematics. D. Van Nostrand Co., Inc., Princeton, N. J.-Toronto-New York-London, 1960xvi+685 MR0123342 0095.12201 Google Scholar Next article FiguresRelatedReferencesCited byDetails Limit Theorems for Random Walks with Absorption4 December 2019 | Journal of Theoretical Probability, Vol. 34, No. 1 Cross Ref A renewal theorem for relatively stable variables21 July 2020 | Bulletin of the London Mathematical Society, Vol. 52, No. 6 Cross Ref Branching processes in a random environment with immigration stopped at zero4 May 2020 | Journal of Applied Probability, Vol. 57, No. 1 Cross Ref Stability of overshoots of zero mean random walksElectronic Journal of Probability, Vol. 25, No. 0 Cross Ref The potential function and ladder heights of a recurrent random walk on $mathbb {Z}$ with infinite varianceElectronic Journal of Probability, Vol. 25, No. none Cross Ref Asymptotically stable random walks of index 1<α<2 killed on a finite setStochastic Processes and their Applications, Vol. 129, No. 12 Cross Ref Notes on random walks in the Cauchy domain of attraction19 November 2018 | Probability Theory and Related Fields, Vol. 175, No. 1-2 Cross Ref Slowly varying functions in the Zygmund sense and generalized regular variationJournal of Mathematical Analysis and Applications, Vol. 475, No. 2 Cross Ref Condensation in critical Cauchy Bienaymé–Galton–Watson treesThe Annals of Applied Probability, Vol. 29, No. 3 Cross Ref On the distribution of a rotationally invariant α-stable process at the hitting time of a given hyperplane22 December 2018 | Reports of the National Academy of Sciences of Ukraine, Vol. 99, No. 12 Cross Ref The weak law of large numbers for nonnegative summands1 February 2019 | Advances in Applied Probability, Vol. 50, No. A Cross Ref On Seneta–Heyde scaling for a stable branching random walk26 July 2018 | Advances in Applied Probability, Vol. 50, No. 2 Cross Ref On the ladder heights of random walks attracted to stable laws of exponent 1Electronic Communications in Probability, Vol. 23, No. none Cross Ref Can one make a laser out of cardboard?The Annals of Applied Probability, Vol. 27, No. 4 Cross Ref On relative stability and weighted laws of large numbers28 September 2016 | Extremes, Vol. 20, No. 1 Cross Ref Strong renewal theorems with infinite mean beyond local large deviationsThe Annals of Applied Probability, Vol. 25, No. 3 Cross Ref Hitting distributions of $alpha$-stable processes via path censoring and self-similarityThe Annals of Probability, Vol. 42, No. 1 Cross Ref An invariance principle for random walk bridges conditioned to stay positiveElectronic Journal of Probability, Vol. 18, No. none Cross Ref A note on summability of ladder heights and the distributions of ladder epochs for random walksStochastic Processes and their Applications, Vol. 121, No. 9 Cross Ref On the probability that integrated random walks stay positiveStochastic Processes and their Applications, Vol. 120, No. 7 Cross Ref Asymptotic properties of multitype critical branching processes evolving in a random environmentDiscrete Mathematics and Applications, Vol. 20, No. 2 Cross Ref Transition phenomena for ladder epochs of random walks with small negative drift1 July 2016 | Advances in Applied Probability, Vol. 41, No. 04 Cross Ref Transition phenomena for ladder epochs of random walks with small negative drift1 July 2016 | Advances in Applied Probability, Vol. 41, No. 4 Cross Ref Local probabilities for random walks conditioned to stay positive4 January 2008 | Probability Theory and Related Fields, Vol. 143, No. 1-2 Cross Ref Weak laws of large numbers for cooperative gamblers28 September 2008 | Periodica Mathematica Hungarica, Vol. 57, No. 1 Cross Ref Regular variation and probability: The early yearsJournal of Computational and Applied Mathematics, Vol. 200, No. 1 Cross Ref Galton--Watson Branching Processes in a Random Environment I: Limit TheoremsV. 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