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Wald's equations, first passage times and moments of ladder variables in Markov random walks

Part of: Stochastic processes Markov processes

Published online by Cambridge University Press:  14 July 2016

Cheng Der Fuh  and
Tze Leung Lai
Cheng Der Fuh*
Affiliation:
Academia Sinica
Tze Leung Lai*
Affiliation:
Stanford University
*
∗Postal address: Institute of Statistical Science, Academia Sinica, Taipei, Taiwan, ROC. Email address: stcheng@ccvax.sinica.edu.tw.
∗∗Postal address: Department of Statistics, Stanford University, Stanford, CA 94305, USA.
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Abstract

Previous work in extending Wald's equations to Markov random walks involves finiteness of moment generating functions and uniform recurrence assumptions. By using a new approach, we can remove these assumptions. The results are applied to establish finiteness of moments of ladder variables and to derive asymptotic expansions for expected first passage times of Markov random walks. Wiener–Hopf factorizations for Markov random walks are also applied to analyse ladder variables and related first passage problems.

Keywords

First passage timeladder height distributionWiener-Hopf factorizationMarkov random walkWald's equations

MSC classification

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory
Secondary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Type
Research Papers
Information
Journal of Applied Probability , Volume 35 , Issue 3 , September 1998 , pp. 566 - 580
Copyright
Copyright © Applied Probability Trust 1998 

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