Asymptotic Log-Harnack inequality and applications for stochastic systems of infinite memory |
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| Institution: | 1. Department of Mathematics, Harbin Institute of Technology, Harbin, China;2. Department of Mathematics and Statistics, University of Strathclyde, Glasgow G1 1XH, UK;1. Department of Mathematics and Statistics, University of Otago, PO Box 56, Dunedin, 9054, New Zealand;2. TU Darmstadt, Angewandte Analysis, Schlossgartenstr. 7, 64289 Darmstadt, Germany;1. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, PR China;2. Department of Mathematics, Wayne State University, Detroit, MI 48202, USA;3. Department of Mathematics, University of Central Florida, Orlando, FL 32828, USA;1. Department of Mathematics, Wayne State University, Detroit, MI 48202, United States;2. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, PR China;1. Center for Applied Mathematics, Tianjin University, Tianjin 300072, China;2. Department of Mathematics, Swansea University, Bay Campus, SA1 8EN, United Kingdom |
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| 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. |
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| Keywords: | Asymptotic Log-Harnack inequality Asymptotic gradient estimate Asymptotic heat kernel Asymptotic irreducibility |
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