IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v88y2000i1p161-174.html
   My bibliography  Save this article

A class of spatially inhomogeneous Dirichlet spaces on the p-adic number field

Author

Listed:
  • Kaneko, Hiroshi

Abstract

In this paper, we will present a method to construct a spatially inhomogeneous process on the p-adic number field. Secondly, we will modify the definition of the derivative of real-valued function on the field, hinted by the Fourier transformation. As a result, we can introduce a class of spatially inhomogeneous modified stable processes, which cannot be obtained by the transformation by multiplicative functional. Lastly, recurrence and transience criteria for the non-local Dirichlet spaces will be presented.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:88:y:2000:i:1:p:161-174
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(99)00124-6
    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.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    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. 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.

    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Urban, Roman, 2012. "Markov processes on the adeles and Dedekind’s zeta function," Statistics & Probability Letters, Elsevier, vol. 82(8), pages 1583-1589.
    6. D. A. Dawson & L. G. Gorostiza, 2018. "Transience and Recurrence of Random Walks on Percolation Clusters in an Ultrametric Space," Journal of Theoretical Probability, Springer, vol. 31(1), pages 494-526, March.
    7. 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.
    8. 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.
    9. 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.
    10. Kumi Yasuda, 2000. "On Infinitely Divisible Distributions on Locally Compact Abelian Groups," Journal of Theoretical Probability, Springer, vol. 13(3), pages 635-657, July.
    11. Yasuda, Kumi, 2013. "Markov processes on the adeles and Chebyshev function," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 238-244.
    12. 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.
    13. Claude Dellacherie & Servet Martinez & Jaime San Martin, 2009. "Ultrametric and Tree Potential," Journal of Theoretical Probability, Springer, vol. 22(2), pages 311-347, June.
    14. 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.
    15. 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.

    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:88:y:2000:i:1:p:161-174. 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.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.