Martingale representations for diffusion processes and backward stochastic differential equations

Zhongmin Qian; ; Jiangang Ying

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arXiv · 0910.4911

Martingale representations for diffusion processes and backward stochastic differential equations

Zhongmin Qian·; Jiangang Ying

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Abstract

In this paper we explain that the natural filtration of a continuous Hunt process is continuous, and show that martingales over such a filtration are continuous. We further establish a martingale representation theorem for a class of continuous Hunt processes under certain technical conditions. In particular we establish the martingale representation theorem for the martingale parts of (reflecting) symmetric diffusions in a bounded domain with a continuous boundary. Together with an approach put forward in Lyons et al(2009), our martingale representation theorem is then applied to the study of initial and boundary problems for quasi-linear parabolic equations by using solutions to backward stochastic differential equations over the filtered probability space determined by reflecting diffusions in a bounded domain with only continuous boundary.

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Zhongmin Qian, ; Jiangang Ying. 2009-10-26. Martingale representations for diffusion processes and backward stochastic differential equations. https://arxiv.org/abs/0910.4911

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