On the well-posedness of a class of McKean Feynman-Kac equations

TL;DR

This paper investigates the well-posedness of McKean Feynman-Kac equations, establishing existence and uniqueness conditions without requiring strong regularity, by linking solutions to semilinear PDEs.

Contribution

It provides new weak and strong existence and uniqueness conditions for MFKEs, connecting their solutions to semilinear PDEs under minimal regularity assumptions.

Findings

Established weak and strong existence conditions.

Proved pathwise uniqueness without strong regularity.

Linked solutions of MFKE to semilinear PDEs.

Abstract

We analyze the well-posedness of a so called McKean Feynman-Kac Equation (MFKE), which is a McKean type equation with a Feynman-Kac perturbation. We provide in particular weak and strong existence conditions as well as pathwise uniqueness conditions without strong regularity assumptions on the coefficients. One major tool to establish this result is a representation theorem relating the solutions of MFKE to the solutions of a nonconservative semilinear parabolic Partial Differential Equation (PDE).