Abstract
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 anaylsis of a linear equation with multiplicativehalf 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.
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Communicated by Ya. G. Sinai
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Bertini, L., Cancrini, N. & Jona-Lasinio, G. The stochastic Burgers Equation. Commun.Math. Phys. 165, 211–232 (1994). https://doi.org/10.1007/BF02099769
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DOI: https://doi.org/10.1007/BF02099769