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

Daniela Morale; Leonardo Tarquini; Stefania Ugolini

arxiv: 2507.23353 · v1 · pith:GNKTY4IZnew · submitted 2025-07-31 · 🧮 math.PR

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

Daniela Morale , Leonardo Tarquini , Stefania Ugolini This is my paper

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keywords associateddifferentialequationmckean-vlasovnon-conservativepath-dependentsolutionconsidered

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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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Signature McKean-Vlasov stochastic differential equations
math.PR 2026-06 unverdicted novelty 6.0

Introduces signature McKean-Vlasov SDEs driven by expected rough path signatures, proves strong well-posedness, approximation of path-dependent equations, and propagation of chaos.