Existence and uniqueness of invariant measures: An approach via sectorial forms

Bogachev V, Röckner M, Zhang TS (2000)
Applied Mathematics and Optimization 41(1): 87-109.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Bogachev, V.; Röckner, MichaelUniBi; Zhang, T.S.
Abstract / Bemerkung
We prove the existence and uniqueness for invariant measures of strongly continuous semigroups on L-2 (X; mu), where X is a (possibly infinite-dimensional) space. Our approach is purely analytic based on the theory of sectorial forms. The generators covered are, e.g., small perturbations (in the sense of sectorial forms) of operators generating hypercontractive semigroups. An essential ingredient of the proofs is a new result on compact embeddings of weighted Sobolev spaces H-1,H-2(rho . dx) on R-d (resp. a Riemannian manifold) into L-2(rho dx). Probabilistic consequences are also briefly discussed.
Stichworte
log-Sobolev inequality; compact embeddings; sectorial forms; invariant measures; inequality; Poincare
Erscheinungsjahr
2000
Zeitschriftentitel
Applied Mathematics and Optimization
Band
41
Ausgabe
1
Seite(n)
87-109
ISSN
0095-4616
Page URI
https://pub.uni-bielefeld.de/record/1621240

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Bogachev V, Röckner M, Zhang TS. Existence and uniqueness of invariant measures: An approach via sectorial forms. Applied Mathematics and Optimization. 2000;41(1):87-109.
Bogachev, V., Röckner, M., & Zhang, T. S. (2000). Existence and uniqueness of invariant measures: An approach via sectorial forms. Applied Mathematics and Optimization, 41(1), 87-109. doi:10.1007/s002459911005
Bogachev, V., Röckner, M., and Zhang, T. S. (2000). Existence and uniqueness of invariant measures: An approach via sectorial forms. Applied Mathematics and Optimization 41, 87-109.
Bogachev, V., Röckner, M., & Zhang, T.S., 2000. Existence and uniqueness of invariant measures: An approach via sectorial forms. Applied Mathematics and Optimization, 41(1), p 87-109.
V. Bogachev, M. Röckner, and T.S. Zhang, “Existence and uniqueness of invariant measures: An approach via sectorial forms”, Applied Mathematics and Optimization, vol. 41, 2000, pp. 87-109.
Bogachev, V., Röckner, M., Zhang, T.S.: Existence and uniqueness of invariant measures: An approach via sectorial forms. Applied Mathematics and Optimization. 41, 87-109 (2000).
Bogachev, V., Röckner, Michael, and Zhang, T.S. “Existence and uniqueness of invariant measures: An approach via sectorial forms”. Applied Mathematics and Optimization 41.1 (2000): 87-109.

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