Non-Archimedean stochastic processes on non-Archimedean manifolds

Abstract

Stochastic processes on manifolds over non-Archimedean fields and with transition measures having values in the field $\bf C$ of complex numbers are defined and investigated. The analogs of Markov, Poisson and Wiener processes are studied. For Poisson processes the non-Archimedean analog of the Lèvy theorem is proved. Stochastic antiderivational equations as well as pseudodifferential equations on manifolds are investigated.