Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10527297 | Stochastic Processes and their Applications | 2016 | 30 Pages |
Abstract
We consider the spatially homogeneous Boltzmann equation for (true) hard and moderately soft potentials. We study the pathwise properties of the stochastic process (Vt)tâ¥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)tâ¥0.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Liping Xu,