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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.

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