The paper proves existence, uniqueness and stability for backward SDEs driven by Brownian motion and a discontinuous rough path of finite q-variation, lifting solution and driver into a Skorokhod-type decorated path space, and derives well-posedness for the corresponding backward doubly SDEs.
Friz, Alexey Korepanov, and Ian Melbourne, Superdiffusive limits for deterministic fast-slow dynamical systems , Probability Theory and Related Fields 178 (2020), no
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Rough backward SDEs with discontinuous Young drivers
The paper proves existence, uniqueness and stability for backward SDEs driven by Brownian motion and a discontinuous rough path of finite q-variation, lifting solution and driver into a Skorokhod-type decorated path space, and derives well-posedness for the corresponding backward doubly SDEs.