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On the existence of submultiplicative moments for the stationary distributions of some Markovian random walks

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

M. S. Sgibnev
M. S. Sgibnev*
Affiliation:
Russian Academy of Sciences
*
∗Postal address: Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk 90, 630090 Russia. Email address: sgibnev@math.nsc.ru.
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Abstract

This paper is concerned with submultiplicative moments for the stationary distributions π of some Markov chains taking values in ℝ+ or ℝ which are closely related to the random walks generated by sequences of independent identically distributed random variables. Necessary and sufficient conditions are given for ∫φ(x)π(dx) < ∞, where φ(x) is a submultiplicative function, i.e. φ(0) = 1 and φ(x+y) ≤ φ(x)φ(y) for all x, y.

Keywords

Oscillating random walkgeneralized Lindley processstationary distributionrandom walksupremumsubmultiplicative functionsmoments

MSC classification

Primary: 60J05: Discrete-time Markov processes on general state spaces
Type
Research Papers
Information
Journal of Applied Probability , Volume 36 , Issue 1 , March 1999 , pp. 78 - 85
Copyright
Copyright © Applied Probability Trust 1999 

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Footnotes

This research was supported by Grant 96-01-01939 of the Russian Foundation for Fundamental Research.

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