THE STOCHASTIC BURGERS-EQUATION

We study Burgers Equation perturbed by a white noise in space and time . We prove the existence of solutions by showing that the Cole-Hopf tr ansformation is meaningful also in the stochastic case. The problem is thus reduced to the analysis of a linear equation with multiplicative half white noise. An explicit solution of the latter is constructed t hrough a generalized Feynman-Kac formula. Typical properties of the tr ajectories are then discussed. A technical result, concerning the regu larizing effect of the convolution with the heat kernel, is proved for stochastic integrals.