A Feynman-Kac result via Markov BSDEs with generalised drivers

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.