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Home / Stochastics: An International Journal of Probability and Stochastic Processes, Volume 81, Number 5

A new approach to the martingale representation theorem

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We prove the martingale representation theorem for Brownian motion, with an explicit expression for the integrand for random variables of the form [image omitted] . We introduce a new stochastic Sobolev space and reformulate the martingale representation theorem in terms of elements from this space.

Keywords: Sobolev space; Wiener functionals; conditional expectations; martingale representation; stochastic Sobolev space; stochastic integral representation

Document Type: Research Article

Affiliations: 1: Department of Mathematics, University of California, San Diego, La Jolla, CA, USA 2: Indian Statistical Institute, Bangalore Centre, Bangalore, India

Publication date: 01 October 2009

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