The stochastic Burgers Equation |
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Authors: | L. Bertini N. Cancrini G. Jona-Lasinio |
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Affiliation: | (1) Dipartimento di Fisica, Università di Roma La Sapienza, P.le Aldo Moro 2, 00185 Roma, Italy;(2) Dipartimento di Matematica, Università di Roma Tor Vergata, Via delle Ricerca Scientifica, 00133 Roma, Italy;(3) Centro Linceo Interdisciplinare, Via della Lungaro 10, I-00165 Roma, Italy |
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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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