Reflected Mckean-Vlasov stochastic differential equations with jumps in time-dependent domains
Probability
2024-06-11 v1
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.
Keywords
Cite
@article{arxiv.2406.05807,
title = {Reflected Mckean-Vlasov stochastic differential equations with jumps in time-dependent domains},
author = {Imane Jarni and Badr Missaoui and Youssef Ouknine},
journal= {arXiv preprint arXiv:2406.05807},
year = {2024}
}