A limit theorem for p-adic-valued probability distributions

Abstract

Listen

Translate article

Probability models in which probabilities, defined in the sense of von Mises as limits of relative frequencies, can belong to p-adic number fields appeared in connection with the problem of the probabilistic interpretation of wave functions in p-adic-valued quantum mechanics and field theory. Here we present a variant of axiomatic p-adic probability theory in the framework of the theory of analytic distributions on p-adic spaces. We prove a theorem on the existence of p-adic-valued probability distributions on p-adic sequences and obtain a limit theorem for sums of independent random variables (an analogue of the law of large numbers).