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Journal Articles Bernoulli Year : 2020

A Feynman-Kac result via Markov BSDEs with generalized driver

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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Dates and versions

hal-01786119 , version 1 (05-05-2018)
hal-01786119 , version 2 (16-07-2019)

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Elena Issoglio, Francesco Russo. A Feynman-Kac result via Markov BSDEs with generalized driver. Bernoulli, 2020, 26, pp.728-766. ⟨10.3150/19-BEJ1150⟩. ⟨hal-01786119v2⟩
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