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Random walks in a quarter plane with zero drifts: transience and recurrence

Part of: Stochastic processes

Published online by Cambridge University Press:  14 July 2016

I. M. Asymont ,
G. Fayolle  and
Μ. V. Menshikov
I. M. Asymont*
Affiliation:
Moscow State University
G. Fayolle*
Affiliation:
INRIA
Μ. V. Menshikov*
Affiliation:
Moscow State University
*
∗Postal address: Moscow State University, Mechanico-Mathematical Faculty, Chair of Probability, Laboratory of Large Random Systems, Vorobyevy Gori, 119899 Moscow, Russia.
∗∗Postal address: INRIA, Domaine de Voluceau, Rocquencourt, BP 105, 78153 Le Chesnay Cedex, France.
∗Postal address: Moscow State University, Mechanico-Mathematical Faculty, Chair of Probability, Laboratory of Large Random Systems, Vorobyevy Gori, 119899 Moscow, Russia.
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Abstract

In this paper we continue the study of the classification problem for random walks in the quarter plane, with zero drifts in the interior of the domain. The necessary and sufficient conditions for these random walks to be ergodic were found earlier in [3]. Here we obtain necessary and sufficient conditions for transience by constructing suitable Lyapounov functions.

Keywords

LYAPOUNOV FUNCTIONTRANSIENCE CONDITIONS

MSC classification

Secondary: 60G42: Martingales with discrete parameter
Type
Research Papers
Information
Journal of Applied Probability , Volume 32 , Issue 4 , December 1995 , pp. 941 - 955
Copyright
Copyright © Applied Probability Trust 1995 

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References

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