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Ergodicity for neutral type SDEs with infinite length of memory

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  • Jianhai Bao
  • Feng‐Yu Wang
  • Chenggui Yuan

Abstract

In this paper, the weak Harris theorem developed in [18] is illustrated by using a straightforward Wasserstein coupling, which implies the exponential ergodicity of the functional solutions to a range of neutral type SDEs with infinite length of memory. A concrete example is presented to illustrate the main result.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:mathna:v:293:y:2020:i:9:p:1675-1690
    DOI: 10.1002/mana.201800539
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    References listed on IDEAS

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    1. 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.
    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. Mattingly, J. C. & Stuart, A. M. & Higham, D. J., 2002. "Ergodicity for SDEs and approximations: locally Lipschitz vector fields and degenerate noise," Stochastic Processes and their Applications, Elsevier, vol. 101(2), pages 185-232, October.
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    Cited by:

    1. 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.
    2. Shukai Chen & Rongjuan Fang & Xiangqi Zheng, 2023. "Wasserstein-Type Distances of Two-Type Continuous-State Branching Processes in Lévy Random Environments," Journal of Theoretical Probability, Springer, vol. 36(3), pages 1572-1590, September.

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