Open Access
November 2019 Functional CLT for martingale-like nonstationary dependent structures
Florence Merlevède, Magda Peligrad, Sergey Utev
Bernoulli 25(4B): 3203-3233 (November 2019). DOI: 10.3150/18-BEJ1088


In this paper, we develop non-stationary martingale techniques for dependent data. We shall stress the non-stationary version of the projective Maxwell–Woodroofe condition, which will be essential for obtaining maximal inequalities and functional central limit theorem for the following examples: nonstationary $\rho$-mixing sequences, functions of linear processes with non-stationary innovations, locally stationary processes, quenched version of the functional central limit theorem for a stationary sequence, evolutions in random media such as a process sampled by a shifted Markov chain.


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Florence Merlevède. Magda Peligrad. Sergey Utev. "Functional CLT for martingale-like nonstationary dependent structures." Bernoulli 25 (4B) 3203 - 3233, November 2019.


Received: 1 April 2018; Revised: 1 August 2018; Published: November 2019
First available in Project Euclid: 25 September 2019

zbMATH: 07110136
MathSciNet: MR4010953
Digital Object Identifier: 10.3150/18-BEJ1088

Keywords: $\rho$-mixing arrays , dependent structures , functional central limit theorem , non-stationary triangular arrays , Projective criteria

Rights: Copyright © 2019 Bernoulli Society for Mathematical Statistics and Probability

Vol.25 • No. 4B • November 2019
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