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Slow diffusion by Markov random flights

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  • Kolesnik, Alexander D.

Abstract

We present a conception of the slow diffusion processes in the Euclidean spaces Rm,m≥1, based on the theory of random flights with small constant speed that are driven by a homogeneous Poisson process of small rate. The slow diffusion condition that, on long time intervals, leads to the stationary distributions, is given. The stationary distributions of slow diffusion processes in some Euclidean spaces of low dimensions, are presented.

Suggested Citation

  • Kolesnik, Alexander D., 2018. "Slow diffusion by Markov random flights," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 499(C), pages 186-197.
    • Handle: RePEc:eee:phsmap:v:499:y:2018:i:c:p:186-197
    DOI: 10.1016/j.physa.2018.02.013
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    References listed on IDEAS

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    1. Weiss, George H, 2002. "Some applications of persistent random walks and the telegrapher's equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 311(3), pages 381-410.
    2. Jaume Masoliver & Katja Lindenberg, 2017. "Continuous time persistent random walk: a review and some generalizations," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 90(6), pages 1-13, June.
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    Cited by:

    1. Cinque, Fabrizio & Orsingher, Enzo, 2023. "Random motions in R3 with orthogonal directions," Stochastic Processes and their Applications, Elsevier, vol. 161(C), pages 173-200.

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