数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (6): 2033-2050.doi: 10.1016/S0252-9602(10)60189-0

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A RANDOM TRANSPORT-DIFFUSION EQUATION

胡耀忠   

  1. Department of Mathematics, University of Kansas, Lawrence, Kansas, 66045 USA
  • 收稿日期:2010-08-30 出版日期:2010-11-20 发布日期:2010-11-20

A RANDOM TRANSPORT-DIFFUSION EQUATION

 HU Yao-Zhong   

  1. Department of Mathematics, University of Kansas, Lawrence, Kansas, 66045 USA
  • Received:2010-08-30 Online:2010-11-20 Published:2010-11-20

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.

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

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

中图分类号: 

  • 60G15