Geodesic
$p$-Adic Brownian Motion over $\mathbb Q_p$
Informatics and Automation, Selected topics of mathematical physics and $p$-adic analysis, Tome 265 (2009), pp. 125-141 
K. Kamizono. $p$-Adic Brownian Motion over $\mathbb Q_p$. Informatics and Automation, Selected topics of mathematical physics and $p$-adic analysis, Tome 265 (2009), pp. 125-141. http://geodesic.mathdoc.fr/item/TRSPY_2009_265_a9/
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     author = {K. Kamizono},
     title = {$p${-Adic} {Brownian} {Motion} over $\mathbb Q_p$},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2009_265_a9/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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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