A RANDOM TRANSPORT-DIFFUSION EQUATION

doi:10.1016/S0252-9602(10)60189-0

Abstract

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.

Key words: random vector field, chaos expansion, random transport-diffusion equation, trace, exponential of quadratic functional of Gaussian field

CLC Number:

60G15

HU Yao-Zhong. A RANDOM TRANSPORT-DIFFUSION EQUATION[J].Acta mathematica scientia,Series B, 2010, 30(6): 2033-2050.

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