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Estimates of Certain Exit Probabilities for p-Adic Brownian Bridges

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  • David Weisbart

    (University of California)

Abstract

For each prime p, a diffusion constant together with a positive exponent specify a Vladimirov operator and an associated p-adic diffusion equation. The fundamental solution of this pseudo-differential equation gives rise to a measure on the Skorokhod space of p-adic valued paths that is concentrated on the paths originating at the origin. We calculate the first exit probabilities of paths from balls and estimate these probabilities for the Brownian bridges.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jotpro:v:35:y:2022:i:3:d:10.1007_s10959-021-01099-0
    DOI: 10.1007/s10959-021-01099-0
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    References listed on IDEAS

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    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.
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