## 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

### Keywords:

random walk with continuous time; state space