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arXiv · 2303.10038

Semilinear Feynman-Kac Formulae for $B$-Continuous Viscosity Solutions

Lukas Wessels
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Abstract

We prove the existence of a $B$-continuous viscosity solution for a class of infinite dimensional semilinear partial differential equations (PDEs) using probabilistic methods. Our approach also yields a stochastic representation formula for the solution in terms of a scalar-valued backward stochastic differential equation. The uniqueness is proved under additional assumptions using a comparison theorem for viscosity solutions. Our results constitute the first nonlinear Feynman-Kac formula using the notion of $B$-continuous viscosity solutions and thus introduces a framework allowing for generalizations to the case of fully nonlinear PDEs.

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Lukas Wessels. 2023-03-17. Semilinear Feynman-Kac Formulae for $B$-Continuous Viscosity Solutions. https://doi.org/10.1080/07362994.2024.2434735

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