IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v53y1994i1p1-22.html
   My bibliography  Save this article

A random walk on p-adics--the generator and its spectrum

Author

Listed:
  • Albeverio, Sergio
  • Karwowski, Witold

Abstract

We construct a random walk with continuous time taking values in the p-adic numbers. We compute its transition semigroup and infinitesimal generator and exhibits its spectrum. We also give the associated Dirichlet form, which is of the jump type.

Suggested Citation

  • Albeverio, Sergio & Karwowski, Witold, 1994. "A random walk on p-adics--the generator and its spectrum," Stochastic Processes and their Applications, Elsevier, vol. 53(1), pages 1-22, September.
    • Handle: RePEc:eee:spapps:v:53:y:1994:i:1:p:1-22
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0304-4149(94)90054-X
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

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

    Citations

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


    Cited by:

    1. David Weisbart, 2022. "Estimates of Certain Exit Probabilities for p-Adic Brownian Bridges," Journal of Theoretical Probability, Springer, vol. 35(3), pages 1878-1897, September.
    2. David Aldous & Steven N. Evans, 1999. "Dirichlet Forms on Totally Disconnected Spaces and Bipartite Markov Chains," Journal of Theoretical Probability, Springer, vol. 12(3), pages 839-857, July.
    3. Sergio Albeverio & Xuelei Zhao, 2001. "A Decomposition Theorem for Lévy Processes on Local Fields," Journal of Theoretical Probability, Springer, vol. 14(1), pages 1-19, January.
    4. Urban, Roman, 2012. "Markov processes on the adeles and Dedekind’s zeta function," Statistics & Probability Letters, Elsevier, vol. 82(8), pages 1583-1589.
    5. Albeverio, Sergio & Karwowski, Witold & Zhao, Xuelei, 1999. "Asymptotics and spectral results for random walks on p-adics," Stochastic Processes and their Applications, Elsevier, vol. 83(1), pages 39-59, September.
    6. Kaneko, Hiroshi, 2000. "A class of spatially inhomogeneous Dirichlet spaces on the p-adic number field," Stochastic Processes and their Applications, Elsevier, vol. 88(1), pages 161-174, July.
    7. Cruz-López, Manuel & Estala-Arias, Samuel & Murillo-Salas, Antonio, 2016. "A random walk on the profinite completion of Z," Statistics & Probability Letters, Elsevier, vol. 109(C), pages 130-138.
    8. Yasuda, Kumi, 2013. "Markov processes on the adeles and Chebyshev function," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 238-244.
    9. Kumi Yasuda, 2000. "On Infinitely Divisible Distributions on Locally Compact Abelian Groups," Journal of Theoretical Probability, Springer, vol. 13(3), pages 635-657, July.
    10. Cruz-López, Manuel & Estala-Arias, Samuel, 2018. "A random walk on the profinite completion of a finitely generated group," Statistics & Probability Letters, Elsevier, vol. 143(C), pages 7-16.
    11. Claude Dellacherie & Servet Martinez & Jaime San Martin, 2009. "Ultrametric and Tree Potential," Journal of Theoretical Probability, Springer, vol. 22(2), pages 311-347, June.
    12. Kumi Yasuda, 2010. "Markov Processes on the Adeles and Representations of Euler Products," Journal of Theoretical Probability, Springer, vol. 23(3), pages 748-769, September.
    13. Hiroshi Kaneko & Xuelei Zhao, 2006. "Transition Semi–groups on a Local Field Induced by Galois Group and their Representation," Journal of Theoretical Probability, Springer, vol. 19(1), pages 221-234, January.
    14. Erik Bakken & David Weisbart, 2019. "Continuous Time p-Adic Random Walks and Their Path Integrals," Journal of Theoretical Probability, Springer, vol. 32(2), pages 781-805, June.
    15. Kaneko, Hiroshi & Tsuzuki, Yoichi, 2011. "A lift of spatially inhomogeneous Markov process to extensions of the field of p-adic numbers," Stochastic Processes and their Applications, Elsevier, vol. 121(2), pages 394-405, February.

    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:spapps:v:53:y:1994:i:1:p:1-22. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    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.