A Feynman–Kac result via Markov BSDEs with generalised drivers

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.

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Authors/Creators:	Issoglio, E https://orcid.org/0000-0003-3035-2712 Russo, F
Copyright, Publisher and Additional Information:	© 2020 ISI/BS. Reproduced in accordance with the publisher's self-archiving policy.
Keywords:	backward stochastic differential equations (BSDEs); distributional driver; Feynman–Kac formula; generalised and rough coefficients; pointwise product; weak Dirichlet process
Dates:	Accepted: 6 August 2019 Published (online): 26 November 2019 Published: February 2020
Institution:	The University of Leeds
Academic Units:	The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Statistics (Leeds)
Depositing User:	Symplectic Publications
Date Deposited:	08 Aug 2019 11:16
Last Modified:	25 Jun 2023 21:56
Status:	Published
Publisher:	Bernoulli Society for Mathematical Statistics and Probability
Identification Number:	https://doi.org/10.3150/19-BEJ1150

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A Feynman–Kac result via Markov BSDEs with generalised drivers

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