IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v269y1999i1p79-89.html
   My bibliography  Save this article

Discrete random walk models for symmetric Lévy–Feller diffusion processes

Author

Listed:
  • Gorenflo, Rudolf
  • Fabritiis, Gianni De
  • Mainardi, Francesco

Abstract

We propose a variety of models of random walk, discrete in space and time, suitable for simulating stable random variables of arbitrary index α (0<α⩽2), in the symmetric case. We show that by properly scaled transition to vanishing space and time steps our random walk models converge to the corresponding continuous Markovian stochastic processes which we refer to as Lévy–Feller diffusion processes.

Suggested Citation

  • Gorenflo, Rudolf & Fabritiis, Gianni De & Mainardi, Francesco, 1999. "Discrete random walk models for symmetric Lévy–Feller diffusion processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 269(1), pages 79-89.
    • Handle: RePEc:eee:phsmap:v:269:y:1999:i:1:p:79-89
    DOI: 10.1016/S0378-4371(99)00082-5
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437199000825
    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/S0378-4371(99)00082-5?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. West, Bruce J. & Seshadri, V., 1982. "Linear systems with Lévy fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 113(1), pages 203-216.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Gorenflo, Rudolf & Mainardi, Francesco & Moretti, Daniele & Pagnini, Gianni & Paradisi, Paolo, 2002. "Fractional diffusion: probability distributions and random walk models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 305(1), pages 106-112.
    2. Silvia Vitali & Iva Budimir & Claudio Runfola & Gastone Castellani, 2019. "The Role of the Central Limit Theorem in the Heterogeneous Ensemble of Brownian Particles Approach," Mathematics, MDPI, vol. 7(12), pages 1-9, November.
    3. Paradisi, Paolo & Cesari, Rita & Mainardi, Francesco & Tampieri, Francesco, 2001. "The fractional Fick's law for non-local transport processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 293(1), pages 130-142.
    4. Agarwal, Ritu & Kritika, & Purohit, Sunil Dutt, 2021. "Mathematical model pertaining to the effect of buffer over cytosolic calcium concentration distribution," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).

    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. West, Bruce J., 1996. "Lévy statistics of water wave forces," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 230(3), pages 359-363.
    2. Hongler, Max-Olivier & Filliger, Roger & Blanchard, Philippe, 2006. "Soluble models for dynamics driven by a super-diffusive noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(2), pages 301-315.
    3. Janicki, Aleksander & Weron, Aleksander, 1995. "Computer simulation of attractors in stochastic models with α-stable noise," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 39(1), pages 9-19.
    4. Paradisi, Paolo & Cesari, Rita & Mainardi, Francesco & Tampieri, Francesco, 2001. "The fractional Fick's law for non-local transport processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 293(1), pages 130-142.
    5. Gorenflo, Rudolf & Mainardi, Francesco & Moretti, Daniele & Pagnini, Gianni & Paradisi, Paolo, 2002. "Fractional diffusion: probability distributions and random walk models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 305(1), pages 106-112.

    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:269:y:1999:i:1:p:79-89. 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.