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

摘要

Stochastic processes on topological vector spaces over non-Archimedean fieldsand with transition measures having values in non-Archimedean fields aredefined and investigated. For this the non-Archimedean analog of the Kolmogorovtheorem is proved. The analogos of Markov and Poisson processes are studied.For Poisson processes the corresponding Poisson measures are considered and thenon-Archimedean analog of the L\`evy theorem is proved. Wide classes ofstochastic processes are constructed.