Mckean-Vlasov stochastic differential equations with oblique reflection on non-smooth time dependent domains

TL;DR

This paper studies McKean-Vlasov stochastic differential equations with oblique reflection in non-smooth, time-dependent domains, establishing existence, uniqueness, propagation of chaos, and a large deviations principle.

Contribution

It introduces new existence and uniqueness results for these equations in complex domains and extends large deviations principles to this setting.

Findings

Proved existence and uniqueness of solutions.

Established propagation of chaos.

Derived a large deviations principle.

Abstract

In this paper, we consider a class of Mckean-Vlasov stochastic differential equation with oblique reflection over an non-smooth time dependent domain. We establish the existence and uniqueness results of this class, address the propagation of chaos and prove a Fredlin-Wentzell type large deviations principle (LDP). One of the main difficulties is raised by the setting of non-smooth time dependent domain. To prove the LDP, a sufficient condition for the weak convergence method, which is suitable for Mckean-Vlasov stochastic differential equation, plays an important role.