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arXiv · 1803.11106

Functional CLT for martingale-like nonstationary dependent structures

Florence Merlevède·Magda Peligrad·Sergey Utev
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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 \r{ho}-mixing sequences, functions of linear processes with non-stationary innovations, 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. 2018-03-29. Functional CLT for martingale-like nonstationary dependent structures. https://arxiv.org/abs/1803.11106

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