White Noise Analysis Approach to Clark Formula

[[abstract]]The representation of functionals of Brownian motion in terms of stochastic integral with respect to Brownian motion is known as Clark formula. In this paper, we are devoted to the derivation of Clark formula for a given generalized white noise functional. A generalized white noise functional F is said to have a Clark representation in the generalized sense on an interval I if there exist a kernel KF such that F = E[F] + ∫I KF(t) dB(t), where the equality holds in the the generalized sense or, equivalently, the equality holds under the S-transform. Examples of Clark representation of generalized white noise functional are given in this paper