Asymptotic Analysis of Distributions in Problems with Two Boundaries. I

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Previous article Next article Asymptotic Analysis of Distributions in Problems with Two Boundaries. IV. I. LotovV. I. Lotovhttps://doi.org/10.1137/1124059PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] V. I. Lotov, Complete asymptotic expansions in two-boundary problems for random walks, Dokl. Akad. Nauk SSSR, 232 (1977), 280–283 MR0428463 0379.60065 Google Scholar[2] V. I. Lotov, Asymptotic analysis in problems with two boundaries for random walks, I, II, Dep. VINITI, No. 3188–76 (35 pp), No. 3189–76 (30 pp.), (In Russian.) Google Scholar[3] A. A. Borovkov and , B. A. Rogozin, Boundary-value problems for some two-dimensional random walks, Teor. Verojatnost. i Primenen, 9 (1964), 401–430 MR0169299 Google Scholar[4] J. H. B. Kemperman, A Wiener-Holf type method for a general random walk with a two-sided boundary, Ann. Mat. Statist., 34 (1963), 1168–1193 MR0155364 0124.33604 CrossrefGoogle Scholar[5A] A. A. Borovkov, Limit theorems on the distributions of maxima of sums of bounded lattice random variables, I, Theory Prob. Appl., 5 (1960), 125–155 10.1137/1105014 0106.12603 LinkGoogle Scholar[5B] A. A. Borovkov, Limit theorems on the distributions of maxima of sums of bounded lattice random variables, II, Theory Prob. Appl., 5 (1960), 341–355 10.1137/1105035 0094.32403 LinkGoogle Scholar[6] A. A. Borovkov, New limit theorems in boundary-value problems for sums of independent terms, Sibirsk. Mat. Ž., 3 (1962), 645–694 MR0145568 Google Scholar[7] A. A. Borovkov, The factorization identities and distribution properties of the supremum of sequential sums, Teor. Verojatnost. i Primenen., 15 (1970), 377–418 MR0283842 0233.60048 Google Scholar[8] V. S. Korolyuk, Asymptotic analysis of distributions of maximum deviations in a lattice random walk, Theory Prob. Appl., 7 (1962), 383–401 10.1137/1107037 0119.14202 LinkGoogle Scholar[9] Yu. V. Borovskih, Complete asymptotic expansions for random walks with two boundaries that are continuous from below (above). I, Zap. Naučn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI), 55 (1976), 64–101, 200 MR0410933 0363.60055 Google Scholar[10] William Feller, An introduction to probability theory and its applications. Vol. I, John Wiley and Sons, Inc., New York, 1957xv+461 MR0088081 0077.12201 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Inequalities in a Two-Sided Boundary Crossing Problem for Stochastic Processes27 May 2021 | Siberian Mathematical Journal, Vol. 62, No. 3 Cross Ref Properties of factorization operators in boundary crossing problems for random walksIzvestiya: Mathematics, Vol. 83, No. 5 Cross Ref О свойствах факторизационных операторов в граничных задачах для случайных блужданий23 September 2019 | Известия Российской академии наук. Серия математическая, Vol. 83, No. 5 Cross Ref Approximation of the expectation of the first exit time from an interval for a random walk29 March 2016 | Siberian Mathematical Journal, Vol. 57, No. 1 Cross Ref On the Asymptotics of the Ruin ProbabilityV. I. Lotov25 March 2015 | Theory of Probability & Its Applications, Vol. 59, No. 1AbstractPDF (162 KB)R Cross Ref On Random Walks in a StripV. I. Lotov17 July 2006 | Theory of Probability & Its Applications, Vol. 36, No. 1AbstractPDF (502 KB)R Cross Ref Summary of Papers Presented at Sessions of the Seminar on Probability Theory and Mathematical Statistics at the Mathematical Institute of the Siberian Section of the USSR Academy of Sciences, 198017 July 2006 | Theory of Probability & Its Applications, Vol. 26, No. 3AbstractPDF (912 KB) Volume 24, Issue 3| 1980Theory of Probability & Its Applications History Submitted:04 July 1977Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1124059Article page range:pp. 480-491ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics