Analysis reveals existence of solutions in McKean-Vlasov SDEs with implications for well-posedness and regularity in path-dependent PDEs.
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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Morale et al. (2025) studied this question.
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