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Some asymptotic results for transient random walks

Part of: Markov processes

Published online by Cambridge University Press:  01 July 2016

J. Bertoin  and
R. A. Doney
J. Bertoin*
Affiliation:
Université Paris VI
R. A. Doney*
Affiliation:
University of Manchester
*
* Postal address: Laboratoire de Probabilités (CNRS), Université Paris VI, 4 Place Jussieu, 75252 Paris Cedex 05, France.
** Postal address: Statistical Laboratory, Department of Mathematics, University of Manchester, M13 9PL, UK.
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Abstract

We consider a real-valued random walk S which drifts to –∞ and is such that E(exp θS1) < ∞ for some θ > 0, but for which Cramér's condition fails. We investigate the asymptotic tail behaviour of the distributions of the all time maximum, the upwards and downwards first passage times and the last passage times. As an application, we obtain new limit theorems for certain conditional laws.

Keywords

TRANSIENT RANDOM WALKS

MSC classification

Secondary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 28 , Issue 1 , March 1996 , pp. 207 - 226
Copyright
Copyright © Applied Probability Trust 1996 

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