Asymptotic Log-Harnack Inequality and Applications for Stochastic Systems of Infinite Memory
Probability
2018-09-10 v2
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.
Keywords
Cite
@article{arxiv.1710.01042,
title = {Asymptotic Log-Harnack Inequality and Applications for Stochastic Systems of Infinite Memory},
author = {Jianhai Bao and Feng-Yu Wang and Chenggui Yuan},
journal= {arXiv preprint arXiv:1710.01042},
year = {2018}
}
Comments
24 pages