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Conditional limit theorems for a left-continuous random walk

Published online by Cambridge University Press:  14 July 2016

A. G. Pakes
A. G. Pakes*
Affiliation:
Monash University
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Abstract

The present work considers a left-continuous random walk moving on the positive integers and having an absorbing state at the origin. Limit theorems are derived for the position of the walk at time n given: (a) absorption does not occur until after n, or (b) absorption does not occur until after m + n where m is very large, or (c) absorption occurs at m + n. A limit theorem is given for an R-positive recurrent Markov chain on the non-negative integers with an absorbing origin and subject to condition (c) above.

Keywords

ABSORBING RANDOM WALKLIMIT THEOREMSSTABLE AND QUASI-STATIONARY DISTRIBUTIONS
Type
Research Papers
Information
Journal of Applied Probability , Volume 10 , Issue 1 , March 1973 , pp. 39 - 53
Copyright
Copyright © Applied Probability Trust 1973 

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