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The continuous time random walk, still trendy: fifty-year history, state of art and outlook

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  • Ryszard Kutner

    (Faculty of Physics, University of Warsaw)

  • Jaume Masoliver

    (Departament de Fisica Matèria Condensada and Institute of Complex Systems, Universitat de Barcelona)

Abstract

In this article we demonstrate the very inspiring role of the continuous-time random walk (CTRW) formalism, the numerous modifications permitted by its flexibility, its various applications, and the promising perspectives in the various fields of knowledge. A short review of significant achievements and possibilities is given. However, this review is still far from completeness. We focused on a pivotal role of CTRWs mainly in anomalous stochastic processes discovered in physics and beyond. This article plays the role of an extended announcement of the Eur. Phys. J. B Special Issue [ http://epjb.epj.org/open-calls-for-papers/123-epj-b/1090-ctrw-50-years-on ] containing articles which show incredible possibilities of the CTRWs.

Suggested Citation

  • Ryszard Kutner & Jaume Masoliver, 2017. "The continuous time random walk, still trendy: fifty-year history, state of art and outlook," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 90(3), pages 1-13, March.
    • Handle: RePEc:spr:eurphb:v:90:y:2017:i:3:d:10.1140_epjb_e2016-70578-3
    DOI: 10.1140/epjb/e2016-70578-3
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    Cited by:

    1. Gatto, R., 2018. "Saddlepoint approximation to the distribution of the total distance of the von Mises–Fisher continuous time random walk," Applied Mathematics and Computation, Elsevier, vol. 324(C), pages 285-294.
    2. Arkashov, N.S., 2022. "On the model of random walk with multiple memory structure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 603(C).
    3. Angeli, Letizia & Grosskinsky, Stefan & Johansen, Adam M., 2021. "Limit theorems for cloning algorithms," Stochastic Processes and their Applications, Elsevier, vol. 138(C), pages 117-152.
    4. Michelitsch, Thomas M. & Polito, Federico & Riascos, Alejandro P., 2021. "On discrete time Prabhakar-generalized fractional Poisson processes and related stochastic dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 565(C).
    5. Aleksejus Kononovicius & Vygintas Gontis, 2019. "Approximation of the first passage time distribution for the birth-death processes," Papers 1902.00924, arXiv.org.
    6. Jewgeni H. Dshalalow & Ryan T. White, 2021. "Current Trends in Random Walks on Random Lattices," Mathematics, MDPI, vol. 9(10), pages 1-38, May.
    7. Ponta, Linda & Trinh, Mailan & Raberto, Marco & Scalas, Enrico & Cincotti, Silvano, 2019. "Modeling non-stationarities in high-frequency financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 173-196.
    8. Jaros{l}aw Klamut & Tomasz Gubiec, 2018. "Directed Continuous-Time Random Walk with memory," Papers 1807.01934, arXiv.org.
    9. Paekivi, Sander & Mankin, Romi, 2019. "Bimodality of the interspike interval distributions for subordinated diffusion models of integrate-and-fire neurons," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    10. Danish A Ahmed & Ali R Ansari & Mudassar Imran & Kamal Dingle & Michael B Bonsall, 2021. "Mechanistic modelling of COVID-19 and the impact of lockdowns on a short-time scale," PLOS ONE, Public Library of Science, vol. 16(10), pages 1-20, October.
    11. Jaume Masoliver & Miquel Montero & Josep Perelló, 2021. "Jump-Diffusion Models for Valuing the Future: Discounting under Extreme Situations," Mathematics, MDPI, vol. 9(14), pages 1-26, July.
    12. Michelitsch, Thomas M. & Riascos, Alejandro P., 2020. "Continuous time random walk and diffusion with generalized fractional Poisson process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    13. Rytis Kazakevicius & Aleksejus Kononovicius & Bronislovas Kaulakys & Vygintas Gontis, 2021. "Understanding the nature of the long-range memory phenomenon in socioeconomic systems," Papers 2108.02506, arXiv.org, revised Aug 2021.

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