Strong approximation of partial sums under dependence conditions with application to dynamical systems

Florence Merlevède (1) , Emmanuel Rio (2, 3)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
2 ALEA - Advanced Learning Evolutionary Algorithms
3 LMV - Laboratoire de Mathématiques de Versailles

In this paper, we obtain precise rates of convergence in the strong invariance principle for stationary sequences of real-valued random variables satisfying weak dependence conditions including strong mixing in the sense of Rosenblatt (1956) as a special case. Applications to unbounded functions of intermittent maps are given.

Domaines: Probabilités [math.PR]

Florence Merlevède, Emmanuel Rio. Strong approximation of partial sums under dependence conditions with application to dynamical systems. 2011. ⟨hal-00672852⟩