IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v154y2022ics0960077921009607.html
   My bibliography  Save this article

Classification of random trajectories based on the fractional Lévy stable motion

Author

Listed:
  • Janczura, Joanna
  • Burnecki, Krzysztof
  • Muszkieta, Monika
  • Stanislavsky, Aleksander
  • Weron, Aleksander

Abstract

In this paper we propose a new approach for the analysis of experimental data based on the fractional Lévy stable motion (FLSM) and apply it to the Golding–Cox mRNA dataset. The FLSM takes into account non-Gaussian α-stable distributions and is characterized by the memory parameter d=H−1/α, where H is the Hurst exponent. The sign of d indicates the type of diffusion: d=0 for Lévy diffusion, d<0 for subdiffusion and d>0 for superdiffusion. By estimating the memory parameter for trajectories, we obtain their classification along the x and y coordinates independently. It appears that most of the trajectories are subdiffusive, other follow the Lévy-diffusion, but none of them is superdiffusive. We also justify presence of the non-Gaussian α-stable distribution by five different goodness-of-fit tests. We note that the classification procedure presented here can be applied to other experimental data which exhibit a non-Gaussian behavior.

Suggested Citation

  • Janczura, Joanna & Burnecki, Krzysztof & Muszkieta, Monika & Stanislavsky, Aleksander & Weron, Aleksander, 2022. "Classification of random trajectories based on the fractional Lévy stable motion," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    • Handle: RePEc:eee:chsofr:v:154:y:2022:i:c:s0960077921009607
    DOI: 10.1016/j.chaos.2021.111606
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077921009607
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2021.111606?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. Gorka Muñoz-Gil & Giovanni Volpe & Miguel Angel Garcia-March & Erez Aghion & Aykut Argun & Chang Beom Hong & Tom Bland & Stefano Bo & J. Alberto Conejero & Nicolás Firbas & Òscar Garibo i Orts & Aless, 2021. "Objective comparison of methods to decode anomalous diffusion," Nature Communications, Nature, vol. 12(1), pages 1-16, December.
    2. Agnieszka Wyłomańska & D Robert Iskander & Krzysztof Burnecki, 2020. "Omnibus test for normality based on the Edgeworth expansion," PLOS ONE, Public Library of Science, vol. 15(6), pages 1-36, June.
    3. Muszkieta, Monika & Janczura, Joanna & Weron, Aleksander, 2021. "Simulation and tracking of fractional particles motion. From microscopy video to statistical analysis. A Brownian bridge approach," Applied Mathematics and Computation, Elsevier, vol. 396(C).
    4. Loch-Olszewska, Hanna, 2019. "Properties and distribution of the dynamical functional for the fractional Gaussian noise," Applied Mathematics and Computation, Elsevier, vol. 356(C), pages 252-271.
    5. Yann Lanoiselée & Nicolas Moutal & Denis S. Grebenkov, 2018. "Diffusion-limited reactions in dynamic heterogeneous media," Nature Communications, Nature, vol. 9(1), pages 1-16, December.
    6. Krzysztof Burnecki & Agnieszka Wylomanska & Aleksei Chechkin, 2015. "Discriminating between Light- and Heavy-Tailed Distributions with Limit Theorem," PLOS ONE, Public Library of Science, vol. 10(12), pages 1-23, December.
    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. Mutothya, Nicholas Mwilu & Xu, Yong, 2021. "Mean first passage time for diffuse and rest search in a confined spherical domain," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 567(C).
    2. Jabłońska-Sabuka, Matylda & Teuerle, Marek & Wyłomańska, Agnieszka, 2017. "Bivariate sub-Gaussian model for stock index returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 628-637.
    3. Song, Wanqing & Duan, Shouwu & Zio, Enrico & Kudreyko, Aleksey, 2022. "Multifractional and long-range dependent characteristics for remaining useful life prediction of cracking gas compressor," Reliability Engineering and System Safety, Elsevier, vol. 225(C).
    4. Hanieh Panahi, 2016. "Model Selection Test for the Heavy-Tailed Distributions under Censored Samples with Application in Financial Data," IJFS, MDPI, vol. 4(4), pages 1-14, December.
    5. Shi, Hong-Da & Du, Lu-Chun & Huang, Fei-Jie & Guo, Wei, 2022. "Collective topological active particles: Non-ergodic superdiffusion and ageing in complex environments," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    6. Guo, Wei & Liu, Ying-Zhou & Huang, Fei-Jie & Shi, Hong-Da & Du, Lu-Chun, 2023. "Brownian particles in a periodic potential corrugated by disorder: Anomalous diffusion and ergodicity breaking," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    7. Marcin Pitera & Aleksei Chechkin & Agnieszka Wyłomańska, 2022. "Goodness-of-fit test for $$\alpha$$ α -stable distribution based on the quantile conditional variance statistics," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(2), pages 387-424, June.
    8. Gajda, Janusz & Bartnicki, Grzegorz & Burnecki, Krzysztof, 2018. "Modeling of water usage by means of ARFIMA–GARCH processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 644-657.
    9. Wang, Xiaolong & Feng, Jing & Liu, Qi & Li, Yongge & Xu, Yong, 2022. "Neural network-based parameter estimation of stochastic differential equations driven by Lévy noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 606(C).
    10. Vitaly Promyslov & Kirill Semenkov, 2021. "Non-Statistical Method for Validation the Time Characteristics of Digital Control Systems with a Cyclic Processing Algorithm," Mathematics, MDPI, vol. 9(15), pages 1-16, July.
    11. Qiao, Le & Ilow, Nicholas & Ignacio, Maxime & Slater, Gary W., 2022. "An empirical method to characterize displacement distribution functions for anomalous and transient diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 604(C).
    12. Giuricich, Mario Nicoló & Burnecki, Krzysztof, 2019. "Modelling of left-truncated heavy-tailed data with application to catastrophe bond pricing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 498-513.
    13. Kelty-Stephen, Damian G. & Mangalam, Madhur, 2023. "Multifractal descriptors ergodically characterize non-ergodic multiplicative cascade processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 617(C).
    14. Agnieszka Wyłomańska & D Robert Iskander & Krzysztof Burnecki, 2020. "Omnibus test for normality based on the Edgeworth expansion," PLOS ONE, Public Library of Science, vol. 15(6), pages 1-36, June.
    15. Muszkieta, Monika & Janczura, Joanna, 2023. "A compressed sensing approach to interpolation of fractional Brownian trajectories for a single particle tracking experiment," Applied Mathematics and Computation, Elsevier, vol. 446(C).
    16. dos Santos, M.A.F. & Colombo, E.H. & Anteneodo, C., 2021. "Random diffusivity scenarios behind anomalous non-Gaussian diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    17. Szczurek, Andrzej & Maciejewska, Monika & Wyłomańska, Agnieszka & Sikora, Grzegorz & Balcerek, Michał & Teuerle, Marek, 2016. "Discrimination of particulate matter emission sources using stochastic methods," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 463(C), pages 452-466.
    18. Gorka Muñoz-Gil & Giovanni Volpe & Miguel Angel Garcia-March & Erez Aghion & Aykut Argun & Chang Beom Hong & Tom Bland & Stefano Bo & J. Alberto Conejero & Nicolás Firbas & Òscar Garibo i Orts & Aless, 2021. "Objective comparison of methods to decode anomalous diffusion," Nature Communications, Nature, vol. 12(1), pages 1-16, December.
    19. Ahamad, Nabi & Debnath, Pallavi, 2020. "Rouse model in crowded environment modeled by “diffusing diffusivity”," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 549(C).
    20. Kumar, A. & Wyłomańska, A. & Połoczański, R. & Sundar, S., 2017. "Fractional Brownian motion time-changed by gamma and inverse gamma process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 648-667.

    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:chsofr:v:154:y:2022:i:c:s0960077921009607. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.