Functional limit theorems for digital expansions
Authors: Drmota, M.; Fuchs, M.; Manstavičius, E.
Source: Acta Mathematica Hungarica, Volume 98, Number 3, February 2002 , pp. 175-201(27)
Abstract:The main purpose of this paper is to discuss the asymptotic behaviour of the difference s q,k(P(n)) - k(q-1)/2 where s q,k (n) denotes the sum of the first k digits in the q-ary digital expansion of n and P(x) is an integer polynomial. We prove that this difference can be approximated by a Brownian motion and obtain under special assumptions on P, a Strassen type version of the law of the iterated logarithm. Furthermore, we extend these results to the joint distribution of q 1-ary and q 2-ary digital expansions where q 1 and q 2 are coprime.
Document Type: Research article
Publication date: 2002-02-01