## Bernoulli

• Bernoulli
• Volume 25, Number 4B (2019), 3203-3233.

### Functional CLT for martingale-like nonstationary dependent structures

#### Abstract

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.

#### Article information

Source
Bernoulli, Volume 25, Number 4B (2019), 3203-3233.

Dates
Revised: August 2018
First available in Project Euclid: 25 September 2019

https://projecteuclid.org/euclid.bj/1569398764

Digital Object Identifier
doi:10.3150/18-BEJ1088

Mathematical Reviews number (MathSciNet)
MR4010953

Zentralblatt MATH identifier
07110136

#### Citation

Merlevède, Florence; Peligrad, Magda; Utev, Sergey. Functional CLT for martingale-like nonstationary dependent structures. Bernoulli 25 (2019), no. 4B, 3203--3233. doi:10.3150/18-BEJ1088. https://projecteuclid.org/euclid.bj/1569398764

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#### Supplemental materials

• Supplement to “Functional CLT for martingale-like nonstationary dependent structures”. The supplementary file Merlevède, Peligrad and Utev [22] contains a detailed proof of Corollary 4.6.