We prove a central limit theorem for strongly mixing sequences under a sharp sufficient condition which combines the rate of the strong mixing coefficient with the quantile function. The result improves on all earlier central limit theorems for this type of dependence and answers a conjecture raised by Bradley in 1997.
Moreover, we derive the corresponding functional central limit theorem.
"The functional central limit theorem under the strong mixing condition." Ann. Probab. 28 (3) 1336 - 1352, July 2000. https://doi.org/10.1214/aop/1019160337