Functional Limit Theorems for Digital Expansions
نویسندگان
چکیده
The main purpose of this paper is to discuss the asymptotic behavior of the difference sq,k(P (n))−k(q−1)/2 where sq,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’s type version of the law of the iterated logarithm. Furthermore, we extend these results to the joint distribution of q1-ary and q2-ary digital expansions where q1 and q2 are coprime.
منابع مشابه
A.D.Wentzell (Tulane University) Limit theorems with asymptotic expansions for stochastic processes. There is a vast riches of limit theorems for sums of independent random variables: theorems about weak convergence, on large deviations, theorems with asymptotic expan-
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