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The averaging method for doubly perturbed distribution dependent SDEs

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  • Ma, Xiaocui
  • Yue, Haitao
  • Xi, Fubao

Abstract

This work studies the averaging method for doubly perturbed distribution dependent SDEs, in which an approximation theorem is established. Using the fixed point theorem, we prove the well-posedness of doubly perturbed distribution dependent SDEs. Then we prove that the solutions of the original equations converge to those of the averaged equations in the sense of mean square and probability. Moreover, an example is provided to show the applications of our results.

Suggested Citation

  • Ma, Xiaocui & Yue, Haitao & Xi, Fubao, 2022. "The averaging method for doubly perturbed distribution dependent SDEs," Statistics & Probability Letters, Elsevier, vol. 189(C).
    • Handle: RePEc:eee:stapro:v:189:y:2022:i:c:s0167715222001389
    DOI: 10.1016/j.spl.2022.109588
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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. Ren, Panpan & Wu, Jiang-Lun, 2021. "Least squares estimation for path-distribution dependent stochastic differential equations," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    3. Chaumont, L. & Doney, R. A., 2000. "Some calculations for doubly perturbed Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 85(1), pages 61-74, January.
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