A quenched weak invariance principle

2012/04/20 by Jérôme Dedecker, Dedecker, Jérôme, Florence Merlevède +3 · 1 citation
Economics, Econometrics and Finance · Mathematics · #60F05 #60F17 #60J05 #Epistemology #FOS: Mathematics #Invariance principle #Mathematical Dynamics and Fractals #Mathematics #Philosophy #Physics #Probability (math.PR) #Statistical physics #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #Theoretical physics #math.PR #msc:60F05 #msc:60F17 #msc:60J05

paper · pdf · doi:10.48550/arxiv.1204.4554

published in arXiv (Cornell University) (Cornell University) · accepted for publication in AIHP

openalex publication_date 2012/04/20 · arxiv created 2013/03/06 · arxiv updated 2013/03/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

In this paper we study the almost sure conditional central limit theorem in its functional form for a class of random variables satisfying a projective criterion. Applications to strongly mixing processes and non irreducible Markov chains are given. The proofs are based on the normal approximation of double indexed martingale-like sequences, a theory which has interest in itself.

Citations

• Martingale approximations for sums of stationary processes

Cited by

• Some remarks on Gordin-Lifšic's condition for martingale approximations

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