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2011 Existence and Uniqueness of Invariant Measures for Stochastic Evolution Equations with Weakly Dissipative Drifts
Wei Liu, Jonas Toelle
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Electron. Commun. Probab. 16: 447-457 (2011). DOI: 10.1214/ECP.v16-1643

Abstract

In this paper, a new decay estimate for a class of stochastic evolution equations with weakly dissipative drifts is established, which directly implies the uniqueness of invariant measures for the corresponding transition semigroups. Moreover, the existence of invariant measures and the convergence rate of corresponding transition semigroup to the invariant measure are also investigated. As applications, the main results are applied to singular stochastic $p$-Laplace equations and stochastic fast diffusion equations, which solves an open problem raised by Barbu and Da Prato in [Stoc. Proc. Appl. 120(2010), 1247-1266].

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Wei Liu. Jonas Toelle. "Existence and Uniqueness of Invariant Measures for Stochastic Evolution Equations with Weakly Dissipative Drifts." Electron. Commun. Probab. 16 447 - 457, 2011. https://doi.org/10.1214/ECP.v16-1643

Information

Accepted: 22 August 2011; Published: 2011
First available in Project Euclid: 7 June 2016

zbMATH: 1244.60062
MathSciNet: MR2831083
Digital Object Identifier: 10.1214/ECP.v16-1643

Subjects:
Primary: 60H15
Secondary: 47D07 , 60J35

Keywords: $p$-Laplace equation , Dissipative , Fast diffusion equation , invariant measure , stochastic evolution equation

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