A Feynman-Kac result via Markov BSDEs with generalized driver

Abstract

In this paper we investigate BSDEs where the driver contains a distributional term (in the sense of generalised functions) and derive general Feynman-Kac formulae related to these BSDEs. We introduce an integral operator to give sense to the equation and then we show the existence of a strong solution employing results on a related PDE.Due to the irregularity of the driver, the $Y$-component of a couple $(Y,Z)$ solving the BSDE is not necessarily a semimartingale but a weak Dirichlet process.

References in corpus (3)

• Forward-backward SDEs with distributional coefficients
• A non-linear parabolic PDE with a distributional coefficient and its applications to stochastic analysis
• BSDEs with no driving martingale, Markov processes and associated Pseudo Partial Differential Equations. Part II: Decoupled mild solutions and Examples