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Reflected Mckean-Vlasov stochastic differential equations with jumps in time-dependent domains
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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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Cited by 1 Pith paper
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Optimal control problem for reflected McKean--Vlasov stochastic differential equations with Poisson jumps
Existence of optimal relaxed controls for reflected McKean-Vlasov SDEs with Poisson jumps is established via moment estimates, Aldous tightness, and Skorokhod map continuity, with strict controls under Roxin convexity.
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