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Optimal strong convergence rate for a class of McKean–Vlasov SDEs with fast oscillating perturbation

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  • Li, Butong
  • Meng, Yongna
  • Sun, Xiaobin
  • Yang, Ting

Abstract

In this paper, we consider the averaging principle for a class of McKean–Vlasov stochastic differential equations perturbed by a fast oscillating term. By using the technique of Poisson equation, we prove the occurrence of the averaging principle, i.e., the solution Xɛ converges to the solution X̄ of the corresponding averaged equation in L2(Ω,C([0,T],Rn)) with the optimal convergence order 1/2. To the best of authors’ knowledge, this is the first result about the strong averaging principle when the coefficients in the slow equation depends on the law of the fast component.

Suggested Citation

  • Li, Butong & Meng, Yongna & Sun, Xiaobin & Yang, Ting, 2022. "Optimal strong convergence rate for a class of McKean–Vlasov SDEs with fast oscillating perturbation," Statistics & Probability Letters, Elsevier, vol. 191(C).
    • Handle: RePEc:eee:stapro:v:191:y:2022:i:c:s0167715222001791
    DOI: 10.1016/j.spl.2022.109662
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    References listed on IDEAS

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    1. Wang, Feng-Yu, 2018. "Distribution dependent SDEs for Landau type equations," Stochastic Processes and their Applications, Elsevier, vol. 128(2), pages 595-621.
    2. Fu, Hongbo & Wan, Li & Liu, Jicheng, 2015. "Strong convergence in averaging principle for stochastic hyperbolic–parabolic equations with two time-scales," Stochastic Processes and their Applications, Elsevier, vol. 125(8), pages 3255-3279.
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