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

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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.

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Acknowledgements

The author is very grateful to the editor and referee for detailed reports and corrections. He also would like to thank Professors Zhao Dong, Renming Song, and Fengyu Wang for their valuable discussions. This work is supported by National Natural Science Foundation of China (Nos. 11501286, 11790272), Natural Science Foundation of Jiangsu Province (No. BK20150564) and CSC.

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Correspondence to Yulin Song.

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Song, Y. Gradient Estimates and Exponential Ergodicity for Mean-Field SDEs with Jumps. J Theor Probab 33, 201–238 (2020). https://doi.org/10.1007/s10959-018-0845-x

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Keywords

  • Malliavin calculus
  • Gradient estimates
  • Exponential ergodicity
  • Density functions
  • McKean–Vlasov equations

Mathematics Subject Classification (2010)

  • 60H07
  • 60H10