On the normal approximation for weakly dependent random variables

Abstract

In this report, we present the estimates of the difference |Eh(Z_n) − Eh(N)|, where Z_n is a sum of n centered and normalized random variables which satisfy the strong mixing condition (without assuming a stationarity), and N is a standard normal random variable for the function h: ℝ → ℝ which is finite and satisfies the Lipschitz condition. In a particular case, the obtained upper bounds are of order O(n^−1/2).