Backward stochastic differential equations with Young drift

TL;DR

This paper establishes the well-posedness of backward stochastic differential equations with a Young drift driven by finite p-variation paths, and applies it to rough PDEs via Feynman-Kac representation.

Contribution

It introduces a direct fixpoint method to prove well-posedness for BSDEs with Young drift, extending existing theory to rough path settings.

Findings

Proves well-posedness of BSDEs with Young drift.

Provides a Feynman-Kac representation for rough PDEs.

Extends classical BSDE theory to rough path context.

Abstract

We prove via a direct fixpoint argument the well-posedness of backward stochastic differential equations containing an additional drift driven by a path of finite $p$-variation with $p \in [1,2)$. An application to the Feynman-Kac representation of semilinear rough partial differential equations is given.