Limit Theorems for Sums of p-Adic Random Variables

Abstract

We study p-adic counterparts of stable distributions, that is limit distributions for sequences of normalized sums of independent identically distributed p-adic-valued random variables. In contrast to the classical case, non-degenerate limit distributions can be obtained only under certain assumptions on the asymptotic behaviour of the number of summands in the approximating sums. This asymptotics determines the ``exponent of stability''.