Asymptotic Log-Harnack Inequality and Applications for Stochastic Systems of Infinite Memory

Abstract

The asymptotic log-Harnack inequality is established for several different models of stochastic differential systems with infinite memory: non-degenerate SDEs, Neutral SDEs, semi-linear SPDEs, and stochastic Hamiltonian systems. As applications, the following properties are derived for the associated segment Markov semigroups: asymptotic heat kernel estimate; uniqueness of the invariant probability measure; asymptotic gradient estimate and hence, asymptotically strong Feller property; and asymptotic irreducibilty.

24 pages

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
• Degenerate SDE with Hölder-Dini Drift and Non-Lipschitz Noise Coefficient