Diffusion approximation for the advection of particles in a strongly turbulent random environment
成果类型：
Article
署名作者：
Komorowski, T
署名单位：
New York University
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
发表日期：
1996
页码：
346-376
关键词：
摘要：
In this paper we prove several theorems concerning the motion of a particle in a random environment. The trajectory of a particle is the solution of the differential equation dx(t)/dt = V(x(t)), where V(x) = v + epsilon(1-alpha) F(x), 0 less than or equal to alpha < 1, v is a constant vector, F is a mean-zero fluctuation field and epsilon(1-alpha) is a parameter measuring the size of the fluctuations. We show that both in case of a motion of a single particle and of a particle system considered in the macroscopic coordinate system moving along with velocity v [i.e., x similar to (x - vt)/epsilon(alpha), t similar to t/epsilon(2)] the diffusion approximation holds provided that F is divergence free. Moreover we show how to renormalize trajectories to obtain a similar result for non-divergence-free fields. These results generalize theorems due to Khasminskii and to Kesten and Papanicolaou.