Asymptotic Log-Harnack inequality and applications for stochastic systems of infinite memory

Jianhai Bao, Feng-Yu Wang and Chenggui Yuan

Stochastic Processes and their Applications, 2019, vol. 129, issue 11, 4576-4596

Abstract: The asymptotic log-Harnack inequality is established for several kinds of models on 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 (hence, asymptotically strong Feller property), as well as asymptotic irreducibility.

Keywords: Asymptotic Log-Harnack inequality; Asymptotic gradient estimate; Asymptotic heat kernel; Asymptotic irreducibility (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (5)

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DOI: 10.1016/j.spa.2018.12.010

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