A Feynman-Kac result via Markov BSDEs with generalised drivers

Elena Issoglio and Francesco Russo
january, 2020
Publication type:
Paper in peer-reviewed journals
Bernoulli, vol. 26, pp. 728-766
assets/images/icons/icon_arxiv.png 1805.02466
Keywords :
Backward stochastic differential equations (BSDEs); distributional driver; weak Dirichlet process; pointwise product; generalised and rough coefficient; Feynman-Kac formula.
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.
    author={Elena Issoglio and Francesco Russo },
    title={A Feynman-Kac result via Markov BSDEs with generalised drivers },
    doi={10.3150/19-BEJ1150 },
    journal={Bernoulli },
    year={2020 },
    volume={26 },