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Further criteria for positive Harris recurrence of Markov chains


Authors: Onésimo Hernández-Lerma and Jean B. Lasserre
Journal: Proc. Amer. Math. Soc. 129 (2001), 1521-1524
MSC (1991): Primary 60J10, 28A33; Secondary 28C15
DOI: https://doi.org/10.1090/S0002-9939-00-05672-0
Published electronically: October 24, 2000
MathSciNet review: 1712909
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Abstract | References | Similar Articles | Additional Information

Abstract:

We provide several necessary and sufficient conditions for a Markov chain on a general state space to be positive Harris recurrent. The conditions only concern asymptotic properties of the expected occupation measures.


References [Enhancements On Off] (What's this?)

  • 1. Glynn P.W. Some topics in regenerative steady-state simulation, Acta Appl. Math. 34, pp. 225-236, 1994. MR 94m:60208
  • 2. Hernández-Lerma O., Lasserre J.B. Ergodic theorems and ergodic decomposition for Markov chains, Acta. Appl. Math. 54, pp. 99-119, 1998.
  • 3. Lasota A., Mackey M.C. Chaos, Fractals and Noise, $2$nd ed., Springer-Verlag, New York, 1994. MR 94j:58102
  • 4. Meyn S.P., Tweedie R.L.Markov Chains and Stochastic Stability, Springer-Verlag, London, 1993. MR 95j:60103
  • 5. Nummelin E. General Irreducible Markov Chains and Non-negative Operators, Cambridge University Press, Cambridge, 1984. MR 87a:60074
  • 6. Revuz. D. Markov Chains, revised edition, North-Holland, Amsterdam, 1984. MR 86a:60097
  • 7. Yosida K. Functional Analysis, $6$th ed., Springer-Verlag, Berlin, 1980. MR 82i:46002

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Additional Information

Onésimo Hernández-Lerma
Affiliation: Departamento de Matemáticas, CINVESTAV-IPN, Apdo. Postal 14-740, México D.F. 07000, Mexico
Email: ohernand@math.cinvestav.mx

Jean B. Lasserre
Affiliation: LAAS-CNRS, 7 Avenue du Colonel Roche, 31077 Toulouse Cédex, France
Email: lasserre@laas.fr

DOI: https://doi.org/10.1090/S0002-9939-00-05672-0
Keywords: Probability measures, setwise convergence, Harris (Markov) chains
Received by editor(s): March 1, 1999
Received by editor(s) in revised form: August 15, 1999
Published electronically: October 24, 2000
Additional Notes: This research was partially supported by the CNRS (France)-CONACYT (México) Scientific Cooperation Program, and by the ECOS (France)-ANUIES (Mexico) Educational and Scientific Cooperation Program.
The first author’s research was also supported by CONACYT Grant 3115P-E9608.
Communicated by: Claudia Neuhauser
Article copyright: © Copyright 2000 American Mathematical Society

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