Non-Archimedean stochastic processes.
Andrei Khrennikov
International Center for Mathematical Modeling
in Physics and Cognitive Sciences,
MSI, University of Växjö, S-35195, Sweden
Sergei Ludkovsky
Institute of General Physics,
Moscow, 119991 GSP-1, Russia
We define and investigate stochastic processes on topological vector spaces
over non-Archimedean fields with
transition measures having values in non-Archimedean fields [1].
The basic result of this paper is the non-Archimedean analog
of the Kolmogorov theorem that gives the possibility
to construct wide classes of stochastic processes
by using finite dimensional
probability distributions. The analogous of Markov
and Poisson processes are studied. For Poisson processes
the corresponding Poisson measures are considered
and the non-Archimedean analog of the Lèvy theorem is proved.
- A. Yu. Khrennikov, p-adic valued distributions in
mathematical physics. (Kluwer Academic Publishers, Dordrecht 1994).