A Feynman-Kac result via Markov BSDEs with generalised drivers

Elena Issoglio; Francesco Russo

doi:10.3150/19-BEJ1150

A Feynman-Kac result via Markov BSDEs with generalised drivers

Elena Issoglio
, Francesco Russo

University of Leeds

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	728-766
Number of pages	39
Journal	Bernoulli
Volume	26
Issue number	1
DOIs	https://doi.org/10.3150/19-BEJ1150
Publication status	Published - 1 Jan 2020

Keywords

Backward stochastic differential equations (BSDEs)
Distributional driver
Feynman-Kac formula
Generalised and rough coefficients
Pointwise product
Weak Dirichlet process

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10.3150/19-BEJ1150

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KW - Backward stochastic differential equations (BSDEs)

KW - Distributional driver

KW - Feynman-Kac formula

KW - Generalised and rough coefficients

KW - Pointwise product

KW - Weak Dirichlet process

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A Feynman-Kac result via Markov BSDEs with generalised drivers

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Keywords

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