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Harnack inequalities for functional SDEs with multiplicative noise and applications

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  • Wang, Feng-Yu
  • Yuan, Chenggui

Abstract

By constructing a new coupling, the log-Harnack inequality is established for the functional solution of a delay stochastic differential equation with multiplicative noise. As applications, the strong Feller property and heat kernel estimates w.r.t. quasi-invariant probability measures are derived for the associated transition semigroup of the solution. The dimension-free Harnack inequality in the sense of Wang (1997) [14] is also investigated.

Suggested Citation

  • Wang, Feng-Yu & Yuan, Chenggui, 2011. "Harnack inequalities for functional SDEs with multiplicative noise and applications," Stochastic Processes and their Applications, Elsevier, vol. 121(11), pages 2692-2710, November.
    • Handle: RePEc:eee:spapps:v:121:y:2011:i:11:p:2692-2710
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    References listed on IDEAS

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    1. Arnaudon, Marc & Thalmaier, Anton & Wang, Feng-Yu, 2009. "Gradient estimates and Harnack inequalities on non-compact Riemannian manifolds," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3653-3670, October.
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    Cited by:

    1. Wang, Zhaojuan & Liu, Meng, 2023. "Periodic measure of a stochastic single-species model in periodic environments," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    2. Zhang, Shao-Qin, 2013. "Harnack inequality for semilinear SPDE with multiplicative noise," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1184-1192.
    3. Wang, Ya & Wu, Fuke & Yin, George & Zhu, Chao, 2022. "Stochastic functional differential equations with infinite delay under non-Lipschitz coefficients: Existence and uniqueness, Markov property, ergodicity, and asymptotic log-Harnack inequality," Stochastic Processes and their Applications, Elsevier, vol. 149(C), pages 1-38.
    4. 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.
    5. Bachmann, Stefan, 2020. "On the strong Feller property for stochastic delay differential equations with singular drift," Stochastic Processes and their Applications, Elsevier, vol. 130(8), pages 4563-4592.
    6. Yong-Hua Mao & Tao Wang, 2022. "Convergence Rates in Uniform Ergodicity by Hitting Times and $$L^2$$ L 2 -Exponential Convergence Rates," Journal of Theoretical Probability, Springer, vol. 35(4), pages 2690-2711, December.
    7. 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.
    8. Yang, Jiangtao, 2022. "Periodic measure of a stochastic non-autonomous predator–prey system with impulsive effects," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 202(C), pages 464-479.
    9. Zong, Gaofeng & Chen, Zengjing, 2013. "Harnack inequality for mean-field stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 83(5), pages 1424-1432.
    10. Wujun Lv & Xing Huang, 2021. "Harnack and Shift Harnack Inequalities for Degenerate (Functional) Stochastic Partial Differential Equations with Singular Drifts," Journal of Theoretical Probability, Springer, vol. 34(2), pages 827-851, June.
    11. Bao, Jianhai & Wang, Feng-Yu & Yuan, Chenggui, 2015. "Hypercontractivity for functional stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 125(9), pages 3636-3656.
    12. Jianhai Bao & Feng‐Yu Wang & Chenggui Yuan, 2020. "Ergodicity for neutral type SDEs with infinite length of memory," Mathematische Nachrichten, Wiley Blackwell, vol. 293(9), pages 1675-1690, September.

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