Probabilistic-statistical models

Classification of infinite divisible distributions over locally compact fields with non-archimedean norms

S. V. Lyudkovskii

Moscow State Technical University of Radioengineering, Electronics and Automation, Moscow

Abstract: The article is devoted to stochastic processes with values in finite dimensional vector spaces over infinite locally compact fields of zero and positive characteristics with non-trivial non-archimedean norms. Infinite divisible distributions are studied. Theorems about their characteristic functionals are proved. Particular cases are given, as well as non-archimedean analogs of Gaussian and Poisson processes and their generalizations are discussed.

Keywords: stochastic process, infinite divisible distribution, infinite field, non-archimedean norm, characteristic functional.

UDC: 519.216.2, 512.625.5, 517.986

Received: 08.04.2012
Revised: 16.04.2012

Bibliographic databases:

•