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

Florence Merlevède ()
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Florence Merlevède: Université Paris VI

Journal of Theoretical Probability, 2003, vol. 16, issue 3, 625-653

Abstract: 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.

Keywords: Hilbert space; central limit theorem; weak invariance principle; strong mixing sequences; martingale approximation (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1023/A:1025668415566

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