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 (deltaW(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 f1{(W(t1))f2(W(t2))...fn(W(tn)). We introduce a new stochastic Sobolev space and reformulate the Martingale Representation theorem in terms of elements from this space.

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September 28, 2004