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Tr. Mat. Inst. Steklova, 2009, Volume 265, Pages 125–141 (Mi tm827)  

This article is cited in 3 scientific papers (total in 3 papers)

$p$-Adic Brownian Motion over $\mathbb Q_p$

K. Kamizono

Faculty of Economics, Nagasaki University, Nagasaki, Japan

Abstract: In this paper, we generalize the result of Bikulov and Volovich (1997) and construct a $p$-adic Brownian motion over $\mathbb Q_p$. First, we construct directly a $p$-adic white noise over $\mathbb Q_p$ by using a specific complete orthonormal system of $\mathbb L^2(\mathbb Q_p)$. A $p$-adic Brownian motion over $\mathbb Q_p$ is then constructed by the Paley–Wiener method. Finally, we introduce a $p$-adic random walk and prove a theorem on the approximation of a $p$-adic Brownian motion by a $p$-adic random walk.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2009, 265, 115–130

Bibliographic databases:

UDC: 519.21
Received in September 2008
Language: English

Citation: K. Kamizono, “$p$-Adic Brownian Motion over $\mathbb Q_p$”, Selected topics of mathematical physics and $p$-adic analysis, Collected papers, Tr. Mat. Inst. Steklova, 265, MAIK Nauka/Interperiodica, Moscow, 2009, 125–141; Proc. Steklov Inst. Math., 265 (2009), 115–130

Citation in format AMSBIB
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\by K.~Kamizono
\paper $p$-Adic Brownian Motion over $\mathbb Q_p$
\inbook Selected topics of mathematical physics and $p$-adic analysis
\bookinfo Collected papers
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\yr 2009
\vol 265
\pages 125--141
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Zuniga-Galindo W.A., “the Non-Archimedean Stochastic Heat Equation Driven By Gaussian Noise”, J. Fourier Anal. Appl., 21:3 (2015), 600–627  crossref  mathscinet  zmath  isi  elib  scopus
    2. Zuniga-Galindo W.A., “Non-Archimedean White Noise, Pseudodifferential Stochastic Equations, and Massive Euclidean Fields”, J. Fourier Anal. Appl., 23:2 (2017), 288–323  crossref  mathscinet  zmath  isi  scopus
    3. Dragovich B. Khrennikov A.Yu. Kozyrev S.V. Volovich I.V. Zelenov E.I., “P-Adic Mathematical Physics: the First 30 Years”, P-Adic Numbers Ultrametric Anal. Appl., 9:2 (2017), 87–121  crossref  mathscinet  zmath  isi  scopus
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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