DIFFUSION LIMIT FOR MANY PARTICLES IN A PERIODIC STOCHASTIC ACCELERATION FIELD

• 成果类型: Article
• 署名作者: Elskens, Yves; Pardoux, Etienne
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite; Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/09-AAP671
• 发表日期: 2010
• 页码: 2022-2039
• 关键词: turbulence; waves

摘要

The one-dimensional motion of any number N of particles in the field of many independent waves (with strong spatial correlation) is formulated as a second-order system of stochastic differential equations, driven by two Wiener processes. In the limit of vanishing particle mass m -> 0, or, equivalently, of large noise intensity, we show that the momenta of all N particles converge weakly to N independent Brownian motions, and this convergence holds even if the noise is periodic. This justifies the usual application of the diffusion equation to a family of particles in a unique stochastic force field. The proof rests on the ergodic properties of the relative velocity of two particles in the scaling limit.