## Electronic Communications in Probability

### Existence and Uniqueness of Invariant Measures for Stochastic Evolution Equations with Weakly Dissipative Drifts

#### 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].

#### Article information

Source
Electron. Commun. Probab., Volume 16 (2011), paper no. 40, 447-457.

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

https://projecteuclid.org/euclid.ecp/1465261996

Digital Object Identifier
doi:10.1214/ECP.v16-1643

Mathematical Reviews number (MathSciNet)
MR2831083

Zentralblatt MATH identifier
1244.60062

Rights

#### Citation

Liu, Wei; Toelle, Jonas. Existence and Uniqueness of Invariant Measures for Stochastic Evolution Equations with Weakly Dissipative Drifts. Electron. Commun. Probab. 16 (2011), paper no. 40, 447--457. doi:10.1214/ECP.v16-1643. https://projecteuclid.org/euclid.ecp/1465261996

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