The averaging method for doubly perturbed distribution dependent SDEs

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. (C) 2022 Elsevier B.V. All rights reserved.

Automated summary

This work investigates the averaging method for doubly perturbed distribution dependent SDEs and establishes an approximation theorem. By using the fixed point theorem, the well-posedness of doubly perturbed distribution dependent SDEs is proven. Furthermore, it is shown that the solutions of the original equations converge to those of the averaged equations in terms of mean square and probability. An example is also provided to demonstrate the practical applications of the results.