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A sufficient condition for the existence of an invariant probability measure for Markov processes

Part of: Stochastic systems and control Markov processes

Published online by Cambridge University Press:  14 July 2016

O. L. V. Costa  and
F. Dufour
O. L. V. Costa*
Affiliation:
Universidade de São Paulo
F. Dufour*
Affiliation:
Université Bordeaux I and Université Bordeaux IV
*
∗Postal address: Departamento de Engenharia de Telecomunicações e Controle, Escola Politécnica da Universidade de São Paulo, São Paulo, 05508 900, Brazil. Email address: oswaldo@lac.usp.br
∗∗Postal address: Mathématiques Appliqées de Bordeaux, Université Bordeaux I, 351 cours de la Liberation, 33405 Talence Cedex, France. Email address: dufour@math.u-bordeaux1.fr
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Abstract

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In this paper, it is shown that the Foster-Lyapunov criterion is sufficient to ensure the existence of an invariant probability measure for both discrete- and continuous-time Markov processes without any additional hypotheses (such as irreducibility).

Keywords

Markov processinvariant probability measureFoster-Lyapunov criterionpetite setdiscrete timecontinuous time

MSC classification

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 93E15: Stochastic stability
Type
Short Communications
Information
Journal of Applied Probability , Volume 42 , Issue 3 , September 2005 , pp. 873 - 878
Copyright
© Applied Probability Trust 2005 

References

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