Stochastic processes on non-Archimedean spaces with values in non-Archimedean fields

2001/10/28 by S. V. Lüdkovsky, S. Ludkovsky, Ludkovsky, S. +3
Economics, Econometrics and Finance · Mathematics · #28C20 (Secondary) #46S10 (Primary) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical and Theoretical Analysis #Stochastic processes and financial applications #advanced mathematical theories #math.CA #msc:28C20 #msc:46S10

paper · pdf · doi:10.48550/arxiv.math/0110305

34 pages

arxiv created 2001/10/28 · openalex publication_date 2001/10/28 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 the non-Archimedean analog of the Kolmogorov theorem is proved. The analogos 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. Wide classes of stochastic processes are constructed.

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