Infinitely divisible distributions over locally compact non-archimedean fields

This paper is devoted to stochastic processes with values in finite-dimensional vector spaces over infinite, locally compact fields of zero and positive characteristics with nontrivial non-Archimedean norms. Infinitely divisible distributions are studied. Theorems about their characteristic functionals are proved. Particular cases are demonstrated as applications to non-Archimedean analogs of Gaussian and Poisson processes and their generalizations.