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February 2020 A Feynman–Kac result via Markov BSDEs with generalised drivers
Elena Issoglio, Francesco Russo
Bernoulli 26(1): 728-766 (February 2020). DOI: 10.3150/19-BEJ1150


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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Elena Issoglio. Francesco Russo. "A Feynman–Kac result via Markov BSDEs with generalised drivers." Bernoulli 26 (1) 728 - 766, February 2020.


Received: 1 March 2019; Revised: 1 July 2019; Published: February 2020
First available in Project Euclid: 26 November 2019

zbMATH: 07140515
MathSciNet: MR4036050
Digital Object Identifier: 10.3150/19-BEJ1150

Keywords: Backward stochastic differential equations (BSDEs) , distributional driver , Feynman–Kac formula , generalised and rough coefficients , pointwise product , weak Dirichlet process

Rights: Copyright © 2020 Bernoulli Society for Mathematical Statistics and Probability

Vol.26 • No. 1 • February 2020
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