Strong Approximations for a Class of Dependent Random Variables with Semi-Exponential Tails

Christophe Cuny (), Jérôme Dedecker () and Florence Merlevède ()
Additional contact information
Christophe Cuny: Univ. Brest, UMR 6205 CNRS, LMBA
Jérôme Dedecker: Université Paris Cité, MAP5, UMR 8145 CNRS
Florence Merlevède: Univ. Gustave Eiffel, Univ. Paris Est Créteil, LAMA, UMR 8050 CNRS

Journal of Theoretical Probability, 2024, vol. 37, issue 3, 2234-2252

Abstract: Abstract We give rates of convergence in the almost sure invariance principle for sums of dependent random variables with semi-exponential tails, whose coupling coefficients decrease at a sub-exponential rate. We show that the rates in the strong invariance principle are in powers of $$\log n$$ log n . We apply our results to iid products of random matrices.

Keywords: Almost sure invariance principle; Coupling; Markov chains; Products of random matrices; 60F17; 60G10; 60J05; 60B15 (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10959-023-01306-0 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jotpro:v:37:y:2024:i:3:d:10.1007_s10959-023-01306-0

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10959

DOI: 10.1007/s10959-023-01306-0

Access Statistics for this article

Journal of Theoretical Probability is currently edited by Andrea Monica

More articles in Journal of Theoretical Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().