Averaging Principle for Doubly Perturbed McKean–Vlasov SDEs With Common Noise

In this article, we address the issue on averaging principle for doubly perturbed McKean–Vlasov stochastic differential equations (SDEs) with common noise under an averaging condition. Employing the Banach fixed point theorem, we establish the well‐posedness of doubly perturbed McKean–Vlasov SDEs with common noise. Under the averaging assumption, we demonstrate that the solutions of the original system converge to those of a simplified time‐homogeneous averaged system in the mean‐square sense. Finally, an example is provided to show the applications of our results.