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.
A hard copy of this manuscript is available from the first-named
author upon request.
The manuscript can also be downloaded in
dvi form (56K),
postscript form (217K),
and pdf form (352K).
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September 28, 2004
