This article is cited in 4 papers

Factorization representations in the boundary crossing problems for random walks on a Markov chain

V. I. Lotov, N. G. Orlova

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: Let $\tau$ be some stopping time for a random walk $S_n$ defined on transitions of a finite Markov chain and let $\tau(t)$ be the first passage time across the level $t$ which occurs after $\tau$. We prove a theorem that establishes a connection between the dual Laplace–Stieltjes transforms of the joint distributions of $(\tau,S_{\tau})$ and $(\tau(t),S_{\tau(t)})$. This result applies to the study of the number of crossings of a strip by sample paths of a random walk.

Keywords: Markov-modulated random walk, factorization representations, boundary crossing problems.

UDC: 519.21

Received: 01.06.2004

 English version: Siberian Mathematical Journal, 2005, 46:4, 661–667

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