  In this paper we express tau functions for the Korteweg de Vries (KdV)
equation, as Laplace transforms of iterated Skorohod integrals. Our main tool
is the notion of Fredholm determinant of an integral operator. Our result
extends the paper of Ikeda and Taniguchi who obtained a stochastic
representation of tau functions for the $N$-soliton solutions of KdV as the
Laplace transform of a quadratic functional of $N$ independent
Ornstein-Uhlenbeck processes. Our general result goes beyond the $N$-soliton
case and enables us to consider a non soliton solution of KdV associated to a
Gaussian process with Cauchy covariance function.
