A random transport-diffusion equation |
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| Authors: | Hu Yaozhong |
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| Institution: | Department of Mathematics, University of Kansas, Lawrence, Kansas, 66045 USA |
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| Abstract: | In this paper we study the integral curve in a random vector field perturbed by white noise. It is related to a stochastic transport-diffusion equation. Under some conditions on the covariance function of the vector field, the solution of this stochastic partial differential equation is proved to have moments. The exact p-th moment is represented through integrals with respect to Brownian motions. The basic tool is Girsanov formula. |
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| Keywords: | random vector field chaos expansion random transport-diffusion equation trace exponential of quadratic functional of Gaussian field |
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