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Invariant sets and ergodic decomposition of local semi-Dirichlet forms

Invariant sets and ergodic decomposition of local semi-Dirichlet forms We prove that weak invariance is equivalent to strong invariance in the framework of quasi-regular local positivity preserving forms with lower bounds. As an application, we give an ergodic decomposition of Markov processes associated with quasi-regular local semi-Dirichlet forms with lower bounds. As consequences, criteria of transience and recurrence for Markov processes associated with quasi-regular semi-Dirichlet forms with lower bounds are presented. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Forum Mathematicum de Gruyter

Invariant sets and ergodic decomposition of local semi-Dirichlet forms

Forum Mathematicum , Volume 23 (6) – Nov 1, 2011

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Publisher
de Gruyter
Copyright
© de Gruyter 2011
ISSN
0933-7741
eISSN
1435-5337
DOI
10.1515/FORM.2011.046
Publisher site
See Article on Publisher Site

Abstract

We prove that weak invariance is equivalent to strong invariance in the framework of quasi-regular local positivity preserving forms with lower bounds. As an application, we give an ergodic decomposition of Markov processes associated with quasi-regular local semi-Dirichlet forms with lower bounds. As consequences, criteria of transience and recurrence for Markov processes associated with quasi-regular semi-Dirichlet forms with lower bounds are presented.

Journal

Forum Mathematicumde Gruyter

Published: Nov 1, 2011

Keywords: Semi-Dirichlet form; Dirichlet form; weakly invariant set; strongly invariant set; irreducibility; strict irreducibility; absolute continuity condition; dissipative part; conservative part; transience; recurrence; ergodic decomposition; Feller diffusion process; strong Feller diffusion process; doubly Feller diffusion process

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