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Gradient Estimates and Exponential Ergodicity for Mean-Field SDEs with Jumps

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  • Yulin Song

    (Nanjing University)

Abstract

In this paper, we study mean-field stochastic differential equations with jumps. By Malliavin calculus for Wiener–Poisson functionals, sharp gradient estimates are derived. Based on the gradient estimates, exponential convergence to the unique invariant measure in total variation distance is also obtained under a dissipative condition.

Suggested Citation

  • Yulin Song, 2020. "Gradient Estimates and Exponential Ergodicity for Mean-Field SDEs with Jumps," Journal of Theoretical Probability, Springer, vol. 33(1), pages 201-238, March.
    • Handle: RePEc:spr:jotpro:v:33:y:2020:i:1:d:10.1007_s10959-018-0845-x
    DOI: 10.1007/s10959-018-0845-x
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    References listed on IDEAS

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    1. Graham, Carl, 1992. "McKean-Vlasov Ito-Skorohod equations, and nonlinear diffusions with discrete jump sets," Stochastic Processes and their Applications, Elsevier, vol. 40(1), pages 69-82, February.
    2. Wang, Feng-Yu, 2018. "Distribution dependent SDEs for Landau type equations," Stochastic Processes and their Applications, Elsevier, vol. 128(2), pages 595-621.
    3. Wang, Feng-Yu, 2011. "Gradient estimate for Ornstein-Uhlenbeck jump processes," Stochastic Processes and their Applications, Elsevier, vol. 121(3), pages 466-478, March.
    4. Mátyás Barczy & Zenghu Li & Gyula Pap, 2015. "Yamada-Watanabe Results for Stochastic Differential Equations with Jumps," International Journal of Stochastic Analysis, Hindawi, vol. 2015, pages 1-23, January.
    5. Benachour, S. & Roynette, B. & Talay, D. & Vallois, P., 1998. "Nonlinear self-stabilizing processes - I Existence, invariant probability, propagation of chaos," Stochastic Processes and their Applications, Elsevier, vol. 75(2), pages 173-201, July.
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    Cited by:

    1. Fan, Xiliang & Huang, Xing & Suo, Yongqiang & Yuan, Chenggui, 2022. "Distribution dependent SDEs driven by fractional Brownian motions," Stochastic Processes and their Applications, Elsevier, vol. 151(C), pages 23-67.
    2. Fan, Xiliang & Yu, Ting & Yuan, Chenggui, 2023. "Asymptotic behaviors for distribution dependent SDEs driven by fractional Brownian motions," Stochastic Processes and their Applications, Elsevier, vol. 164(C), pages 383-415.

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