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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}
}

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24 pages