Zhihui, Liu
Published 2020-07-26Version 1
We derive an asymptotic log-Harnack inequality for nonlinear monotone SPDE driven by possibly degenerate multiplicative noise. Our main tool is the asymptotic coupling by the change of measure. As an application, we show that, under certain monotone and coercive conditions on the coefficients, the corresponding Markov semigroup is asymptotically strong Feller, asymptotic irreducibility, and possesses a unique and thus ergodic invariant measure. The results are applied to highly degenerate finite-dimensional or infinite-dimensional diffusion processes.
Asymptotic Log-Harnack Inequality and Applications for Stochastic Systems of Infinite Memory
On ergodic invariant measures for the stochastic Landau-Lifschitz-Gilbert equation in 1D
Harnack Inequalities, Ergodicity, and Contractivity of Stochastic Reaction-Diffusion Equation in $L^p$
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