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Invariant sets and ergodic decomposition of local semi-Dirichlet forms
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Kazuhiro Kuwae
Published/Copyright:
July 8, 2010
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.
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
Received: 2009-04-07
Revised: 2010-01-13
Published Online: 2010-07-08
Published in Print: 2011-November
© de Gruyter 2011
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Keywords for this article
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
Articles in the same Issue
- Almost global existence for quasilinear wave equations with inhomogeneous terms in 3D
- Heegner points and Eisenstein series
- Discrete components of some complementary series
- Even universal binary Hermitian lattices over imaginary quadratic fields
- Combinatorial classification of piecewise hereditary algebras
- Weighted energy estimates for wave equations in exterior domains
- Invariant sets and ergodic decomposition of local semi-Dirichlet forms
- Regularity in parabolic Dini continuous systems
- The reciprocity law for the twisted second moment of Dirichlet L-functions
