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Continuous time persistent random walk: a review and some generalizations

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  • Jaume Masoliver

    (University of Barcelona)

  • Katja Lindenberg

    (University of California)

Abstract

We review some extensions of the continuous time random walk first introduced by Elliott Montroll and George Weiss more than 50 years ago [E.W. Montroll, G.H. Weiss, J. Math. Phys. 6, 167 (1965)], extensions that embrace multistate walks and, in particular, the persistent random walk. We generalize these extensions to include fractional random walks and derive the associated master equation, namely, the fractional telegrapher’s equation. We dedicate this review to our joint work with George H. Weiss (1930–2017). It saddens us greatly to report the recent death of George Weiss, a scientific giant and at the same time a lovely and humble man.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:eurphb:v:90:y:2017:i:6:d:10.1140_epjb_e2017-80123-7
    DOI: 10.1140/epjb/e2017-80123-7
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    Cited by:

    1. Kononovicius, Aleksejus & Kazakevičius, Rytis & Kaulakys, Bronislovas, 2022. "Resemblance of the power-law scaling behavior of a non-Markovian and nonlinear point processes," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    2. Aleksejus Kononovicius & Rytis Kazakeviv{c}ius & Bronislovas Kaulakys, 2022. "Resemblance of the power-law scaling behavior of a non-Markovian and nonlinear point processes," Papers 2205.07563, arXiv.org, revised Jul 2022.
    3. Kolesnik, Alexander D., 2018. "Slow diffusion by Markov random flights," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 499(C), pages 186-197.
    4. Tawfik, Ashraf M. & Abdelhamid, Hamdi M., 2021. "Generalized fractional diffusion equation with arbitrary time varying diffusivity," Applied Mathematics and Computation, Elsevier, vol. 410(C).

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