Infinitely divisible distributions over locally compact non-archimedean fields

TL;DR

This paper investigates infinitely divisible distributions of stochastic processes over finite-dimensional vector spaces in non-archimedean local fields, establishing key theorems about their characteristic functionals and exploring specific cases.

Contribution

It provides new theoretical results on the structure of infinitely divisible distributions in non-archimedean settings, including characteristic functional theorems and particular case analyses.

Findings

Theorems on characteristic functionals of infinitely divisible distributions

Characterization of distributions over non-archimedean fields

Examples of specific cases analyzed

Abstract

The article is devoted to stochastic processes with values in finite-dimensional vector spaces over infinite locally compact fields with non-trivial non-archimedean valuations. Infinitely divisible distributions are investigated. Theorems about their characteristic functionals are proved. Particular cases are demonstrated.