On the weak invariance principle for non adapted sequences under projective criteria.

Jérôme Dedecker (1) , Florence Merlevède (2) , Dalibor Volny (3)

1 LSTA - Laboratoire de Statistique Théorique et Appliquée
2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
3 LMRS - Laboratoire de Mathématiques Raphaël Salem

In this paper we study the central limit theorem and its weak invariance principle for sums of non adapted stationary sequences, under different normalizations. Our conditions involve the conditional expectation of the variables with respect to a given $\sigma$-algebra, as done in Gordin (1969) and Heyde (1974). These conditions are well adapted to a large variety of examples, including linear processes with dependent innovations or regular functions of linear processes.

Keywords: functions of linear processes; Central limit theorem; weak invariance principle; projective criteria; martingale approximation; functions of linear processes.

Domains: Statistics [math.ST]

Jérôme Dedecker, Florence Merlevède, Dalibor Volny. On the weak invariance principle for non adapted sequences under projective criteria.. 2006. ⟨hal-00022125⟩