Hostname: page-component-745bb68f8f-hvd4g Total loading time: 0 Render date: 2025-01-12T05:32:31.175Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

[AI] Aspandiiarov, S. and Iasnogorodski, R., General criteria of integrability of functions of passage-times for non-negative stochastic processes and their applications, Teor. Veroyatnost. i Primenen, 43 (1998), 509–539.CrossRefGoogle Scholar
[Ch] Chung, K.L., Markov Chains with Stationary Transition Probabilities, Springer-Verlag, Berlin, New York, 1960.Google Scholar
[CK] Carmona, R. and Klein, A., Exponential moments for hitting times of uniformly ergodic Markov processes, Ann. Probab., 11 (1983), 648–655.Google Scholar
[L] Lamperti, J., Criteria for stochastic processes II: passage-time moments, J. Math. Anal. Appl., 7 (1963), 127–145.CrossRefGoogle Scholar
[MW] Menshikov, M. and Williams, R.J., Passage-time moments for continuous non-negative stochastic processes and applications, Adv. Appl. Prob., 28 (1996), 747–762.CrossRefGoogle Scholar
[SS] Shimizu, A. and Soshi, T., Positively recurrent Markov chains and the stepping stone model as a Fleming-Viot process, (submitted).Google Scholar
[TT] Tuominen, P. and Tweedie, R.L., Subgeometric rates of convergence of f-ergodic Markov chains, Adv. Appl. Prob., 26 (1994), 775–798.CrossRefGoogle Scholar