p$-adic Brownian motion

We define p-adic Brownian motion (Wiener process) and study its properties. We construct a presentation of the trajectories of this process by their series expansions with respect to van der Put's basis and show that they are nowhere differentiable functions satisfying the p-adic Lipschitz cond...

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Bibliographic Details
Published in:Izvestiya. Mathematics 2016-01, Vol.80 (6), p.1084-1093
Main Author: Zelenov, E I
Format: Article
Language:English
Subjects:
Brownian motion
Continuity (mathematics)
Functions (mathematics)
Lipschitz condition
Mathematical analysis
Series expansion
Trajectories
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Summary:We define p-adic Brownian motion (Wiener process) and study its properties. We construct a presentation of the trajectories of this process by their series expansions with respect to van der Put's basis and show that they are nowhere differentiable functions satisfying the p-adic Lipschitz condition of order 1. We define the p-adic Wiener measure on the space of continuous functions and study its properties.
ISSN:1064-5632
1468-4810
DOI:10.1070/IM8351