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Limit Theorems for Sums of p-Adic Random Variables

Anatoly N. Kochubei
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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''.

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Anatoly N. Kochubei. 1998-02-14. Limit Theorems for Sums of p-Adic Random Variables. https://arxiv.org/abs/math/9802068

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