A nonlinear parabolic equation with noise - A reduction method

In this paper we study a class of parabolic equations with a nonlinear grad ient term. The system is disturbed by white noise in time. We show that the unique solution of this problem can be represented as the Wick product bet ween a normalized random variable of exponential form and the solution of a nonlinear parabolic equation. We allow random initial data which might be anticipating. A relation between the Wick product with a normalized exponen tial and translation is proved in order to establish our results.