A Feynman-Kac result via Markov BSDEs with generalised drivers
january, 2020
Type de publication :
Article (revues avec comité de lecture)
Journal :
Bernoulli, vol. 26, pp. 728-766
DOI :
HAL :
arXiv :
Mots clés :
Backward stochastic differential equations (BSDEs); distributional driver; weak Dirichlet process; pointwise product; generalised and rough coefficient; Feynman-Kac formula.
Résumé :
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.
BibTeX :
@article{Iss-Rus-2020,
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 },
month={1},
volume={26 },
pages={728--766},
}