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The stochastic Burgers equation. (English) Zbl 0807.60062
Summary: 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 transformation 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 through a generalized Feynman-Kac formula. Typical properties of the trajectories are then discussed. A technical result, concerning the regularizing effect of the convolution with the heat kernel, is proved for stochastic integrals.

60H99 Stochastic analysis
60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
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