About the rate of normal approximation for the distribution of the number of repetitions in a stationary discrete random sequence

Abstract

The paper presents the problem of asymptotic normality of the number of r-fold repetitions of characters in a segment of a (strictly) stationary discrete random sequence on the set {1, 2,..., N} with the uniformly strong mixing property. It is shown that in the case when the uniformly strong mixing coefficient φ(t) for an arbitrarily given α > 0 decreases as t-6-α, then the distance in the uniform metric between the distribution function of the number of repetitions and the distribution function of the standard normal law decreases at a rate of O(n- δ) with increasing sequence length n for any α ∈ (0; α (32 + 4α )-1)).