A Nonlinear Parabolic Equation with Noise

In this paper we study a class of parabolic equations with a nonlinear gradient 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 between 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 exponential and translation is proved in order to establish our results.