Reflected Mckean-Vlasov stochastic differential equations with jumps in time-dependent domains (2406.05807v1)

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.