Electronic Communications in Probability

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

Wei Liu and Jonas Toelle

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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

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

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

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Zentralblatt MATH identifier

Primary: 60H15: Stochastic partial differential equations [See also 35R60]
Secondary: 60J35: Transition functions, generators and resolvents [See also 47D03, 47D07] 47D07: Markov semigroups and applications to diffusion processes {For Markov processes, see 60Jxx}

stochastic evolution equation invariant measure dissipative $p$-Laplace equation fast diffusion equation

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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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