Stochastic processes and their spectral representations over non-archimedean fields

Abstract

The article is devoted to stochastic processes with values in finite- and infinite-dimensional vector spaces over infinite fields $\bf K$ of zero characteristics with non-trivial non-archimedean norms. For different types of stochastic processes controlled by measures with values in $\bf K$ and in complete topological vector spaces over $\bf K$ stochastic integrals are investigated. Vector valued measures and integrals in spaces over $\bf K$ are studied. Theorems about spectral decompositions of non-archimedean stochastic processes are proved.