IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v603y2022ics0378437122005246.html
   My bibliography  Save this article

On the model of random walk with multiple memory structure

Author

Listed:
  • Arkashov, N.S.

Abstract

A model of one-dimensional random walk based on the memory flow phenomenology is constructed. In this model, the jumps of the random walk process have a convolution structure formed on the basis of a finite sequence of memory functions and a stationary, generally speaking, non-Gaussian sequence. A physical interpretation of memory functions and the stationary sequence is given. A limit theorem in the metric space D[0,1] for the normalized walk process is obtained.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:phsmap:v:603:y:2022:i:c:s0378437122005246
    DOI: 10.1016/j.physa.2022.127795
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437122005246
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2022.127795?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Cannon, Michael J. & Percival, Donald B. & Caccia, David C. & Raymond, Gary M. & Bassingthwaighte, James B., 1997. "Evaluating scaled windowed variance methods for estimating the Hurst coefficient of time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 241(3), pages 606-626.
    2. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Wei, Kun & Zhang, Youxin & Luo, Yi, 2018. "Variance-mediated multifractal analysis of group participation in chasing a single dangerous prey," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 1275-1287.
    2. Andrew Clark, 2005. "The use of Hurst and effective return in investing," Quantitative Finance, Taylor & Francis Journals, vol. 5(1), pages 1-8.
    3. Michalski, Sebastian, 2008. "Blocks adjustment—reduction of bias and variance of detrended fluctuation analysis using Monte Carlo simulation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(1), pages 217-242.
    4. Almurad, Zainy M.H. & Delignières, Didier, 2016. "Evenly spacing in Detrended Fluctuation Analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 451(C), pages 63-69.
    5. John Halley & Dimitris Kugiumtzis, 2011. "Nonparametric testing of variability and trend in some climatic records," Climatic Change, Springer, vol. 109(3), pages 549-568, December.
    6. Mukli, Peter & Nagy, Zoltan & Eke, Andras, 2015. "Multifractal formalism by enforcing the universal behavior of scaling functions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 417(C), pages 150-167.
    7. Hartmann, András & Mukli, Péter & Nagy, Zoltán & Kocsis, László & Hermán, Péter & Eke, András, 2013. "Real-time fractal signal processing in the time domain," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(1), pages 89-102.
    8. 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).
    9. Mante, Claude, 2007. "Application of resampling and linear spline methods to spectral and dispersional analyses of long-memory processes," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4308-4323, May.
    10. Mason, David M., 2016. "The Hurst phenomenon and the rescaled range statistic," Stochastic Processes and their Applications, Elsevier, vol. 126(12), pages 3790-3807.
    11. Tan, Pei P. & Galagedera, Don U.A. & Maharaj, Elizabeth A., 2012. "A wavelet based investigation of long memory in stock returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(7), pages 2330-2341.
    12. Emilian Lucian NEACSU & Marcela Daniela TODONI, 2014. "A Way To Determine Chaotic Behaviour In Romanian Stock Market," Review of Economic and Business Studies, Alexandru Ioan Cuza University, Faculty of Economics and Business Administration, issue 14, pages 207-214, December.
    13. Mulligan, Robert F., 2014. "Multifractality of sectoral price indices: Hurst signature analysis of Cantillon effects in disequilibrium factor markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 403(C), pages 252-264.
    14. Aleksejus Kononovicius & Vygintas Gontis, 2019. "Approximation of the first passage time distribution for the birth-death processes," Papers 1902.00924, arXiv.org.
    15. 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).
    16. 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.
    17. Kirchner, M. & Schubert, P. & Schmidtbleicher, D. & Haas, C.T., 2012. "Evaluation of the temporal structure of postural sway fluctuations based on a comprehensive set of analysis tools," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(20), pages 4692-4703.
    18. 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.
    19. Jewgeni H. Dshalalow & Ryan T. White, 2021. "Current Trends in Random Walks on Random Lattices," Mathematics, MDPI, vol. 9(10), pages 1-38, May.
    20. Alvarez-Ramirez, J. & Echeverria, J.C. & Meraz, M. & Rodriguez, E., 2017. "Asymmetric acceleration/deceleration dynamics in heart rate variability," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 479(C), pages 213-224.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:603:y:2022:i:c:s0378437122005246. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.