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

Jianhai Bao, Feng-Yu Wang, Chenggui Yuan

Published 2017-10-03Version 1

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.