Martingale representations for diffusion processes and backward stochastic differential equations

Journal article

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.

Authors: Qian, Z; Ying, J

• Journal: Lecture Notes in Mathematics
• Volume: 2046
• Pages: 75-103
• Publication date: 2009-10-26
• DOI: 10.1007/978-3-642-27461-9_4
• ISSN: 0075-8434
• Language: English
• Keywords: 60H10, 60H30, 60J45; math.PR