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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
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    Citations

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    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. Urban, Roman, 2012. "Markov processes on the adeles and Dedekind’s zeta function," Statistics & Probability Letters, Elsevier, vol. 82(8), pages 1583-1589.
    3. 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.
    4. Kumi Yasuda, 2000. "On Infinitely Divisible Distributions on Locally Compact Abelian Groups," Journal of Theoretical Probability, Springer, vol. 13(3), pages 635-657, July.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Yasuda, Kumi, 2013. "Markov processes on the adeles and Chebyshev function," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 238-244.
    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.

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