Year: 2026
Type: preprint
Abstract: In this paper, we investigate the weak invariance principle in some Besov spaces for strictly stationary sequences. In particular, we provide sufficient conditions on the moments and the dependence of a strictly stationary sequence to guaranty the weak invariance principle in these Besov spaces. Several dependence structures are considered, including projective conditions, $α$-dependent, $ρ$-mixing, and $τ$ -dependent conditions. The main tools in the proofs are martingale approximation and deviation inequalities for weakly dependent sequences. Our results cover a large range of strictly stationary sequences that were not treated previously in the literature. Moreover, the presented conditions are sharp.
Source: arXiv (Cornell University)
Authors: Giraudo, Davide, Sharipov, Sadillo
Institution: Institut de Recherche Mathématique Avancée
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221491678