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Stochastic Analysis and Diffusion Processes$
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Gopinath Kallianpur and P Sundar

Print publication date: 2014

Print ISBN-13: 9780199657063

Published to Oxford Scholarship Online: April 2014

DOI: 10.1093/acprof:oso/9780199657063.001.0001

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Invariant Measures and Ergodicity

Invariant Measures and Ergodicity

Chapter:
(p.292) 11 Invariant Measures and Ergodicity
Source:
Stochastic Analysis and Diffusion Processes
Author(s):

Gopinath Kallianpur

P. Sundar

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199657063.003.0011

Existence of stationary measures and ergodic behavior of stochastic systems form an active and important research area with several applications in engineering, physical and biological sciences. A mean-square ergodic theorem is proved for one-dimensional diffusions. Existence and uniqueness of invariant measures, and ergodicity for Markov processes are established under fairly general hypotheses.

Keywords:   invariant measure, ergodic measure, strong Feller property, irreducibility, invariant set

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