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Diffusion on \(p\)-adic numbers. (English) Zbl 0826.46069

Itô, K. (ed.) et al., Gaussian random fields. Proceedings of the third Nagoya Lévy seminar, held in Nagoya, Japan, 15-20 August, 1990. Singapore: World Scientific. Ser. Probab. Stat. 1, 86-99 (1991).
We give a direct construction of a random walk with continuous time and state space the field of \(p\)-adic numbers.
For the entire collection see [Zbl 0812.00031].

MSC:

46S10 Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis
46N55 Applications of functional analysis in statistical physics
60J60 Diffusion processes
60G50 Sums of independent random variables; random walks
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