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Passage-Time Moments for Positively Recurrent Markov Chains

Published online by Cambridge University Press:  22 January 2016

Tokuzo Shiga ,
Akinobu Shimizu  and
Takahiro Soshi
Tokuzo Shiga
Affiliation:
Department of Mathematics, Tokyo Institute of Technology, Oh-okayama, Tokyo 152-8551, Japan
Akinobu Shimizu
Affiliation:
Institute of Natural Sciences, Nagoya City University, Nagoya 467-8501, Japan
Takahiro Soshi
Affiliation:
Department of Applied Mathematics, Yokohama National University, Yokohama 240-0067, Japan
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Abstract

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Fractional moments of the passage-times are considered for positively recurrent Markov chains with countable state spaces. A criterion of the finiteness of the fractional moments is obtained in terms of the convergence rate of the transition probability to the stationary distribution. As an application it is proved that the passage time of a direct product process of Markov chains has the same order of the fractional moments as that of the single Markov chain.

Keywords

60J27
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 162 , June 2001 , pp. 169 - 185
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2001

References

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