Backward stochastic differential equations with Young drift

Joscha Diehl; Jianfeng Zhang

doi:10.1186/s41546-017-0016-5

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2017, Volume 2: 5. Doi: 10.1186/s41546-017-0016-5

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Backward stochastic differential equations with Young drift

Joscha Diehl^1, , and
Jianfeng Zhang^2, ,

1 Max-Planck Institute for Mathematics in the Sciences, Leipzig, Germany;
2 Department of Mathematics, University of Southern California, Los Angeles, California, USA

Joscha Diehl, diehl@mis.mpg.de ; Jianfeng Zhang, jianfenz@usc.edu

Received: October 28, 2016

Revised: March 26, 2017

Published: September 2020

This research was partially supported by the DAAD P.R.I.M.E. program and NSF grant DMS 1413717.

Abstract / Introduction Related Papers Cited by

Abstract

We show the well-posedness of backward stochastic differential equations containing an additional drift driven by a path of finite q-variation with q ∈[1, 2). In contrast to previous work, we apply a direct fixpoint argument and do not rely on any type of flow decomposition. The resulting object is an effective tool to study semilinear rough partial differential equations via a Feynman-Kac type representation.

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