Martingale
Representation Theorem
### A New Approach to the Martingale
Representation Theorem

#### P.J. Fitzsimmons and B. Rajeev

Let (W(t)) be a Brownian motion. We
represent the distribution-valued process (delta_{W(t)}) as the
solution of an evolution equation. Using this we prove the
Martingale Representation Theorem, with an explicit expression for
the integrand for random variables of the form
f_{1}{(W(t_{1}))f_{2}(W(t_{2}))...f_{n}(W(t_{n})).
We introduce a new stochastic Sobolev space and reformulate the Martingale
Representation theorem in terms of elements from this space.

A hard copy of this manuscript is available from the first-named
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September 28, 2004