Strong approximations for a class of dependent random variables with semi exponential tails

C Cuny (1) , J Dedecker (2) , F Merlevède (3)

1 LMBA - Laboratoire de Mathématiques de Bretagne Atlantique
2 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5
3 LAMA - Laboratoire Analyse et de Mathématiques Appliquées

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 subexponential rate. We show that the rates in the strong invariance principle are in powers of log n. We apply our results to iid products of random matrices.

Mots clés: Almost sure invariance principle; Coupling; Markov chains; products of random matrices

Domaines: Probabilités [math.PR]

C Cuny, J Dedecker, F Merlevède. Strong approximations for a class of dependent random variables with semi exponential tails. 2023. ⟨hal-04100038⟩