Killed path-dependent McKean-Vlasov SDEs for a probabilistic representation of non-conservative McKean PDEs

2025/07/31 by Morale, Daniela, Tarquini, Leonardo, Ugolini, Stefania
#60H10 #60H30 #60J60 #60J75 #60J85 #60K35 #82C22 #82C31 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2507.23353

Abstract

A McKean-Vlasov stochastic differential equation subject to killing associated to a regularised non-conservative and path-dependent nonlinear parabolic partial differential equation is studied. The existence and pathwise uniqueness of a strong solution and the regularity properties of its sub-probability law are proved. The density of such a law may be seen as a weak solution of the considered PDE. The well-posedness of the associated particle system is also discussed.

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