科研之友
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摘要
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
- 出版日期2010-11
