An alternative to the coupling of Berkes-Liu-Wu for strong approximations

Christophe Cuny (1) , Jérôme Dedecker (2) , Florence Merlevède (3)

1 ERIM - Equipe de Recherche en Informatique et Mathématiques
2 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5
3 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

In this paper we propose an alternative to the coupling of Berkes, Liu and Wu [1] to obtain strong approximations for partial sums of dependent sequences. The main tool is a new Rosen-thal type inequality expressed in terms of the coupling coefficients. These coefficients are well suited to some classes of Markov chains or dynamical systems, but they also give new results for smooth functions of linear processes.

Domaines: Probabilités [math.PR]

Christophe Cuny, Jérôme Dedecker, Florence Merlevède. An alternative to the coupling of Berkes-Liu-Wu for strong approximations. Chaos, Solitons & Fractals, 2018, 106, pp.233-242. ⟨10.1016/j.chaos.2017.11.019⟩. ⟨hal-01565627⟩