Representation theorems for backward doubly stochastic differential equations
Probability
2008-11-12 v4
Abstract
In this paper we study the class of backward doubly stochastic differential equations (BDSDEs, for short) whose terminal value depends on the history of forward diffusion. We first establish a probabilistic representation for the spatial gradient of the stochastic viscosity solution to a quasilinear parabolic SPDE in the spirit of the Feynman-Kac formula, without using the derivatives of the coefficients of the corresponding BDSDE. Then such a representation leads to a closed-form representation of the martingale integrand of BDSDE, under only standard Lipschitz condition on the coefficients.
Keywords
Cite
@article{arxiv.0712.2219,
title = {Representation theorems for backward doubly stochastic differential equations},
author = {Auguste Aman},
journal= {arXiv preprint arXiv:0712.2219},
year = {2008}
}
Comments
The version of this article have 20 pages and is submitted to Journal Bernoulli for publication