Limit theorems for the number of successes in random binary sequences with random embeddings

摘要

The sequence of n random (0, l)-variables X_1, ... , X_n is considered, with θ_n of these variables distributed equiprobable and the others take the value 1 with probability p (0< P < 1,p ≠1/2）, θ_n is a random variable taking values 0, 1, ..., n). On the assumption that n → oo and under certain conditions imposed on p, θ_n and X_k, k = 1,..., n, several limit theorems for the sum S_n = ∑_(k=1)~nX_k. The results are of interest in connection with steganography and statistical analysis of sequences produced by random number generators.