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.
"A Feynman–Kac result via Markov BSDEs with generalised drivers." Bernoulli 26 (1) 728 - 766, February 2020. https://doi.org/10.3150/19-BEJ1150