Log-Harnack inequality for reflected SPDEs driven by multiplicative noises and its applications

Abstract

We mainly investigate the log-Harnack inequality for the reflected stochastic partial differential equation driven by multiplicative noises based on the gradient estimate of the associated Markov semigroup. To do it, the penalization method and the comparison principle for stochastic partial differential equations are adopted. As its applications, we also establish the entropy-cost inequality and study some important estimates of the transition density relative to its invariant measure.

References in corpus (4)

• Harnack inequality and applications for stochastic generalized porous media equations
• Harnack Inequalities for Functional SDEs with Multiplicative Noise and Applications
• Harnack inequality for SDE with multiplicative noise and extension to Neumann semigroup on nonconvex manifolds
• Existence of Invariant Measures for Reflected SPDEs

Cited by in corpus (1)

• Existence of Invariant Measures for Reflected SPDEs