Stochastic Processes on Non-Archimedean Spaces with Values in Non-Archimedean Fields,

A. Khrennikov, S. Ludkovsky

2003, v.9, №1, 131-162

ABSTRACT

Stochastic processes on topological vector spaces over non-Archimedean fields and with transition measures having values in non-Archimedean fields are defined and investigated. For this purpose the non-Archimedean analog of the Kolmogorov theorem is proved. The analogs of Markov and Poisson processes are studied. For Poisson processes the corresponding Poisson measures are considered and the non-Archimedean analog of the Levy theorem is proved. Wide classes of stochastic processes are constructed.

Keywords: Markov processes,Levy processes,topological vector spaces over non-Archimedean fields,measures with values in non-Archimedean fields

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