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Asymptotic log-Harnack inequality and applications for SPDE with degenerate multiplicative noise

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  • Hong, Wei
  • Li, Shihu
  • Liu, Wei

Abstract

The asymptotic log-Harnack inequality is established for SPDE with degenerate multiplicative noise by the coupling method. As applications, the gradient estimate, asymptotic strong Feller property, irreducibility, heat kernel estimate and ergodicity are derived.

Suggested Citation

  • Hong, Wei & Li, Shihu & Liu, Wei, 2020. "Asymptotic log-Harnack inequality and applications for SPDE with degenerate multiplicative noise," Statistics & Probability Letters, Elsevier, vol. 164(C).
    • Handle: RePEc:eee:stapro:v:164:y:2020:i:c:s0167715220301139
    DOI: 10.1016/j.spl.2020.108810
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    References listed on IDEAS

    as
    1. Wang, Feng-Yu & Zhang, Tusheng, 2014. "Log-Harnack inequality for mild solutions of SPDEs with multiplicative noise," Stochastic Processes and their Applications, Elsevier, vol. 124(3), pages 1261-1274.
    2. Bao, Jianhai & Wang, Feng-Yu & Yuan, Chenggui, 2019. "Asymptotic Log-Harnack inequality and applications for stochastic systems of infinite memory," Stochastic Processes and their Applications, Elsevier, vol. 129(11), pages 4576-4596.
    3. Zhang, Shao-Qin, 2013. "Harnack inequality for semilinear SPDE with multiplicative noise," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1184-1192.
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