Reflected Mckean-Vlasov stochastic differential equations with jumps in time-dependent domains

TL;DR

This paper studies reflected McKean-Vlasov stochastic differential equations within time-dependent convex domains, establishing existence, uniqueness, stability, and propagation of chaos results for these complex systems.

Contribution

It introduces a novel framework for analyzing reflected McKean-Vlasov SDEs in time-dependent domains, including existence, uniqueness, and stability properties.

Findings

Proved existence and uniqueness of solutions

Established stability with respect to initial conditions

Demonstrated propagation of chaos

Abstract

In this paper, we investigate the deterministic multidimensional Skorokhod problem with normal reflection in a family of time-dependent convex domains that are c\`adl\`ag with respect to the Hausdorff metric. We then show the existence and uniqueness of solutions to multidimensional McKean-Vlasov stochastic differential equations reflected in these time-dependent domains. Additionally, we derive stability properties with respect to the initial condition and the coefficients. Finally, we establish a propagation of chaos result.