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.

中文翻译：

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双扰动分布相关SDE的平均方法

这项工作研究了双摄分布依赖SDE的平均方法，其中建立了一个逼近定理。使用不动点定理，我们证明了双摄分布相关 SDE 的适定性。然后我们证明了原始方程的解收敛于均方和概率意义上的平均方程的解。此外，还提供了一个例子来展示我们的结果的应用。