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

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arxiv 2406.05807 v1 pith:K43GKFJU submitted 2024-06-09 math.PR

Imane Jarni , Badr Missaoui , Youssef Ouknine This is my paper · ORCID
classification math.PR
keywords domainstime-dependentdifferentialequationsmckean-vlasovmultidimensionalreflectedrespect
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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.

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