On the Central Limit Theorem and Its Weak Invariance Principle for Strongly Mixing Sequences with Values in a Hilbert Space via Martingale Approximation

Abstract

In this paper we not only prove an extension to Hilbert spaces of a sharp central limit theorem for strongly real-valued mixing sequences, but also slightly improve it. The proof is mainly based on the Bernstein blocking technique and approximations by martingale differences. Moreover, we derive also the corresponding functional central limit theorem.