4 papers
A Feynman--Kac representation of a non-conservative and path-dependent nonlinear reaction-diffusion-advection system
Daniela Morale, Leonardo Tarquini, Stefania Ugolini
We provide a probabilistic interpretation of a weakly parabolic PDE--ODE system with a reaction term, which makes the dynamics non-conservative. As a consequence, the solution is r…
Signature McKean-Vlasov stochastic differential equations
Fred Espen Benth, Salvador Ortiz-Latorre, Leonardo Tarquini
McKean-Vlasov-type stochastic differential equations (SDEs) are characterized by coefficients depending on both the state and the law of the solution. In this work, we focus on a c…
Path-dependent McKean PDEs with reaction: a discussion on probabilistic interpretations and particle approximations
Daniela Morale, Leonardo Tarquini, Stefania Ugolini
In this paper, we discuss and compare two probabilistic approaches for associating a stochastic differential equation with a McKean-type partial differential equation featuring a r…
Killed path-dependent McKean-Vlasov SDEs for a probabilistic representation of non-conservative McKean PDEs
Daniela Morale, Leonardo Tarquini, Stefania Ugolini
A McKean-Vlasov stochastic differential equation subject to killing associated to a regularised non-conservative and path-dependent nonlinear parabolic partial differential equatio…