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Further criteria for positive Harris recurrence of Markov chains
Author(s):
Onésimo
Hernández-Lerma;
Jean
B.
Lasserre
Journal:
Proc. Amer. Math. Soc.
129
(2001),
1521-1524.
MSC (1991):
Primary 60J10, 28A33;
Secondary 28C15
Posted:
October 24, 2000
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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:
- 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,
 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.
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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:
10.1090/S0002-9939-00-05672-0
PII:
S 0002-9939(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
Posted:
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
Copyright of article:
Copyright
2000,
American Mathematical Society
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