Boundary Problems for Sums of Lattice Random Variables, Defined on a Finite Regular Markov Chain

Previous article Next article Boundary Problems for Sums of Lattice Random Variables, Defined on a Finite Regular Markov ChainE. L. PresmanE. L. Presmanhttps://doi.org/10.1137/1112039PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] A. A. Borovkov, New limit theorems in boundary-value problems for sums of independent terms, Sibirsk. Mat. Ž., 3 (1962), 645–694, (In Russian.) MR0145568 Google Scholar[2] A. A. Borovkov and , B. A. Rogozin, Boundary value problems for some two-dimensional random walks, Theory Prob. Applications, 9 (1964), 361–388, (English translation.) 10.1137/1109055 LinkGoogle Scholar[3] J. Keilson and , D. M. G. Wishart, A central limit theorem for processes defined on a finite Markov chain, Proc. Cambridge Philos. Soc., 60 (1964), 547–567 MR0169271 0126.33504 CrossrefGoogle Scholar[4] J. Keilson and , D. M. G. Wishart, Boundary problems for additive processes defined on a finite Markov chain, Proc. Cambridge Philos. Soc., 61 (1965), 173–190 MR0172319 0138.40703 CrossrefGoogle Scholar[5] I. S. Volkov, On the distribution of sums of random variables defined on a homogeneous Markov chain with finite number of states, Theory Prob. Applications, 3 (1958), 384–399, (English translation.) 10.1137/1103032 LinkGoogle Scholar[6] H. D. Miller, A convexivity property in the theory of random variables defined on a finite Markov chain, Ann. Math. Statist., 32 (1961), 1260–1270 MR0126886 0108.15101 CrossrefGoogle Scholar[7] H. D. Miller, Absorption probabilities for sums of random variables defined on a finite Markov chain, Proc. Cambridge Philos. Soc., 58 (1962), 286–298 MR0140146 0114.33703 CrossrefGoogle Scholar[8] B. A. Rogozin, On the distribution of the first jump, Theory Prob. Applications, 9 (1964), 450–465, (English translation.) 10.1137/1109060 LinkGoogle Scholar[9] I. Ts. Gokhberg, A factorization problem in normed rings, functions of isometric and symmetric operators and singular integral equations, Russian Math. Surveys, 19 (1964), 63–114, (English translation.) 10.1070/rm1964v019n01ABEH004137 0124.07103 CrossrefGoogle Scholar[10] E. L. Presman, On waiting time for many-server queues, Theory Prob. Applications, 10 (1965), 63–73, (English translation.) 10.1137/1110006 0161.15501 LinkGoogle Scholar[11] I. C. Gohberg and , M. G. Krei˘n, Systems of integral equations on the half-line with kernels depending on the difference of the arguments, Uspehi Mat. Nauk (N.S.), 13 (1958), 3–72, (In Russian.) MR0102720 Google Scholar[12] A. A. Borovkov, Some problems on controlled probability processes, Sibirsk. Mat. Ž., 5 (1964), 996–1006, (In Russian.) MR0182051 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Conditioned local limit theorems for random walks defined on finite Markov chains25 October 2019 | Probability Theory and Related Fields, Vol. 176, No. 1-2 Cross Ref Limit theorems for Markov walks conditioned to stay positive under a spectral gap assumptionThe Annals of Probability, Vol. 46, No. 4 Cross Ref Limit theorems for affine Markov walks conditioned to stay positiveAnnales de l'Institut Henri Poincaré, Probabilités et Statistiques, Vol. 54, No. 1 Cross Ref A Survey on Conditioned Limit Theorems for Products of Random Matrices and Affine Random Walks22 November 2017 Cross Ref A monotonically converging algorithm for the severity of ruin in a discrete semi-markov risk modelScandinavian Actuarial Journal, Vol. 2004, No. 5 Cross Ref The severity of ruin in a discrete semi-Markov risk model7 September 2017 | Stochastic Models, Vol. 18, No. 1 Cross Ref Risk theory in a Markovian environmentScandinavian Actuarial Journal, Vol. 1989, No. 2 Cross Ref Symmetric Wiener-Hopf factorisations in Markov additive processesZeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, Vol. 26, No. 2 Cross Ref On the use of a fundamental identity in the theory of semi-Markov queues1 July 2016 | Advances in Applied Probability, Vol. 4, No. 02 Cross Ref On the use of a fundamental identity in the theory of semi-Markov queues1 July 2016 | Advances in Applied Probability, Vol. 4, No. 2 Cross Ref Conditional Poisson processes14 July 2016 | Journal of Applied Probability, Vol. 9, No. 2 Cross Ref Semi-stationary processesZeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, Vol. 23, No. 2 Cross Ref A generalization of a renewal theoremSiberian Mathematical Journal, Vol. 12, No. 3 Cross Ref Volume 12, Issue 2| 1967Theory of Probability & Its Applications History Submitted:12 January 1967Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1112039Article page range:pp. 323-328ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics