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].

http://www.math.washington.edu/~ejpecp/ECP/viewarticle.php?id=2308&layout=abstract

References in corpus (9)

• SPDE in Hilbert Space with Locally Monotone Coefficients
• Large Deviations for Stochastic Evolution Equations with Small Multiplicative Noise
• Random attractors for a class of stochastic partial differential equations driven by general additive noise
• Harnack inequality and applications for stochastic generalized porous media equations
• Stochastic Porous Media Equation and Self-Organized Criticality
• Harnack Inequality and Applications for Stochastic Evolution Equations with Monotone Drifts
• Harnack Inequality and Strong Feller Property for Stochastic Fast-Diffusion Equations
• Estimates for the ergodic measure and polynomial stability of plane stochastic curve shortening flow
• Ergodicity of Stochastic Curve Shortening Flow in the Plane

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• A gradient flow formulation for the stochastic Amari neural field model
• Stochastic evolution equations with singular drift and gradient noise via curvature and commutation conditions
• Exponential Convergence of Non-Linear Monotone SPDEs
• Random attractors for singular stochastic partial differential equations
• Stability and moment estimates for the stochastic singular $\Phi$-Laplace equation
• Improved regularity for the stochastic fast diffusion equation