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Moments for stationary Markov chains with asymptotically zero drift

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Abstract

We consider a Markov chain on ℝ+ with asymptotically zero drift and finite second moments of jumps. We assume that the chain has invariant distribution. The paper is devoted to the existence and nonexistence of moments of invariant distribution. Our analysis is based on the technique of test functions.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    D. A. Korshunov

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  1. D. A. Korshunov
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Correspondence to D. A. Korshunov.

Additional information

Dedicated to my teacher on the occasion of his 80th birthday; the paper is related to my MSc and PhD Theses.

Original Russian Text Copyright © 2011 Korshunov D. A.

The author was supported by the Russian Foundation for Basic Research (Grant 10-01-00161).

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 52, No. 4, pp. 829–840, July–August, 2011.

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Korshunov, D.A. Moments for stationary Markov chains with asymptotically zero drift. Sib Math J 52, 655–664 (2011). https://doi.org/10.1134/S0037446611040100

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  • DOI: https://doi.org/10.1134/S0037446611040100

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