Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



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
Published electronically: October 24, 2000
MathSciNet review: 1712909
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information


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. Peter W. Glynn, Some topics in regenerative steady-state simulation, Acta Appl. Math. 34 (1994), no. 1-2, 225–236. MR 1273856,
  • 2. Hernández-Lerma O., Lasserre J.B. Ergodic theorems and ergodic decomposition for Markov chains, Acta. Appl. Math. 54, pp. 99-119, 1998.
  • 3. Andrzej Lasota and Michael C. Mackey, Chaos, fractals, and noise, 2nd ed., Applied Mathematical Sciences, vol. 97, Springer-Verlag, New York, 1994. Stochastic aspects of dynamics. MR 1244104
  • 4. S. P. Meyn and R. L. Tweedie, Markov chains and stochastic stability, Communications and Control Engineering Series, Springer-Verlag London, Ltd., London, 1993. MR 1287609
  • 5. Esa Nummelin, General irreducible Markov chains and nonnegative operators, Cambridge Tracts in Mathematics, vol. 83, Cambridge University Press, Cambridge, 1984. MR 776608
  • 6. D. Revuz, Markov chains, 2nd ed., North-Holland Mathematical Library, vol. 11, North-Holland Publishing Co., Amsterdam, 1984. MR 758799
  • 7. Kôsaku Yosida, Functional analysis, 6th ed., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 123, Springer-Verlag, Berlin-New York, 1980. MR 617913

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 60J10, 28A33, 28C15

Retrieve articles in all journals with MSC (1991): 60J10, 28A33, 28C15

Additional Information

Onésimo Hernández-Lerma
Affiliation: Departamento de Matemáticas, CINVESTAV-IPN, Apdo. Postal 14-740, México D.F. 07000, Mexico

Jean B. Lasserre
Affiliation: LAAS-CNRS, 7 Avenue du Colonel Roche, 31077 Toulouse Cédex, France

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