Backward doubly stochastic differential equations with random coefficients and quasilinear stochastic PDEs
Probability
2018-10-17 v1
Abstract
In this paper, by virtue of Malliavin calculus, we establish a relationship between backward doubly stochastic differential equations with random coefficients and quasilinear stochastic PDEs, and thus extend the well-known nonlinear stochastic Feynman-Kac formula of Pardoux and Peng [14] to non-Markovian case.
Keywords
Cite
@article{arxiv.1810.06959,
title = {Backward doubly stochastic differential equations with random coefficients and quasilinear stochastic PDEs},
author = {Jiaqiang Wen and Yufeng Shi},
journal= {arXiv preprint arXiv:1810.06959},
year = {2018}
}
Comments
To appear in Journal of Mathematical Analysis and Applications