The multifractal nature of Boltzmann processes

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:126

Article

Xu, Liping¹ 

[1] Univ Paris 06, Lab Probabil & Modeles Aleatoires, UMR 7599, Case 188,4 Pl Jussieu, F-75252 Paris, France

关键词: Kinetic theory;    Boltzmann equation;    Multifractal analysis;   

DOI  :  10.1016/j.spa.2016.01.008

来源: Elsevier

【 摘 要 】

We consider the spatially homogeneous Boltzmann equation for (true) hard and moderately soft potentials. We study the pathwise properties of the stochastic process (Vt)(t >= 0), which describes the time evolution of the velocity of a typical particle. We show that this process is almost surely multifractal and compute its spectrum of singularities. For hard potentials, we also compute the multifractal spectrum of the position process (Xt)(t >= 0). (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free