Rate of convergence in the central limit theorem for random variables with strong mixing (Q762831)

The convergence rate in the central limit theorem is obtained in case the real random variables \(X_ 1,X_ 2,...,X_ n\) have zero mean and satisfy the strong mixing condition together with the following conditions: \(E(X_ 1+X_ 2+...+X_ n)^ 2\geq c_ 0n\) and \(\max_{1\leq j\leq n}E| X_ j|^ s\leq d,\) where \(0<c_ 0<\infty\) and \(2<s\leq 3\). Various rates of decreasing of mixing coefficients are considered. Our results generalize those of \textit{A. N. Tikhomirov} [Teor. Veroyatn. Primen. 25, 800-818 (1980; Zbl 0448.60019); English translation in Theory Probab. Appl. 25, 790-809 (1981)] to the case of not necessary stationary random variables.