The Annals of Probability

Passage-time moments for nonnegative stochastic processes and an application to reflected random walks in a quadrant

S. Aspandiiarov, R. Iasnogorodski, and M. Menshikov

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Abstract

In this paper we get some sufficient conditions for the finiteness or nonfiniteness of the passage-time moments for nonnegative discrete parameter processes. The developed criteria are closely connected with the well-known results of Foster for the ergodicity of Markov chains and are given in terms of sub(super)martingales. Then, as an application of the obtained results, we get explicit conditions for the finiteness or nonfiniteness of passage-time moments for reflected random walks in a quadrant with zero drift in the interior.

Article information

Source
Ann. Probab., Volume 24, Number 2 (1996), 932-960.

Dates
First available in Project Euclid: 11 December 2002

Permanent link to this document
https://projecteuclid.org/euclid.aop/1039639371

Digital Object Identifier
doi:10.1214/aop/1039639371

Mathematical Reviews number (MathSciNet)
MR1404537

Zentralblatt MATH identifier
0869.60036

Subjects
Primary: 60G42: Martingales with discrete parameter 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 60J60: Diffusion processes [See also 58J65]

Keywords
Passage-time recurrence classification reflected random walks

Citation

Aspandiiarov, S.; Iasnogorodski, R.; Menshikov, M. Passage-time moments for nonnegative stochastic processes and an application to reflected random walks in a quadrant. Ann. Probab. 24 (1996), no. 2, 932--960. doi:10.1214/aop/1039639371. https://projecteuclid.org/euclid.aop/1039639371


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References

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