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The multifractal nature of Boltzmann processes

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  • Xu, Liping

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)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.

Suggested Citation

  • Xu, Liping, 2016. "The multifractal nature of Boltzmann processes," Stochastic Processes and their Applications, Elsevier, vol. 126(8), pages 2181-2210.
    • Handle: RePEc:eee:spapps:v:126:y:2016:i:8:p:2181-2210
    DOI: 10.1016/j.spa.2016.01.008
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    Cited by:

    1. Lőrinczi, József & Yang, Xiaochuan, 2019. "Multifractal properties of sample paths of ground state-transformed jump processes," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 83-94.

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