The averaging method for doubly perturbed distribution dependent SDEs

Xiaocui Ma, Haitao Yue and Fubao Xi

Statistics & Probability Letters, 2022, vol. 189, issue C

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.

Keywords: Doubly perturbed distribution dependent SDE; Fixed point theorem; Averaging method; Approximation theorem (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spl.2022.109588

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