Martingale representations for diffusion processes and backward stochastic differential equations

Details Martingale representations for diffusion processes and backward stochastic differential equations Martingale representations for diffusion processes and backward stochastic differential equations

2009-10-26

arxiv.org/abs/0910.4911v1

Mathematics

Probability

28 pages

Scientific paper

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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