Functionals of diffusion processes as stochastic integrals

Abstract

Let be a standard d -dimensional Brownian motion and L a smooth functional on the space C = C d [0, 1] of continuous functions from [0,1] to R d , such that Denote Then is a square integrable martingale which can be represented as a stochastic integral; consequently the random variable has the representation For Fréchet differentiable functions L , Clark(1) gave the following formula for the integrand e :

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