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

Abstract : 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 :
Document type :
Preprints, Working Papers, ...
Domain :

Cited literature [27 references]

https://hal.archives-ouvertes.fr/hal-00022125
Contributor : Florence Merlevède <>
Submitted on : Monday, April 3, 2006 - 10:43:37 AM
Last modification on : Friday, March 27, 2020 - 3:23:33 AM
Long-term archiving on: : Wednesday, September 8, 2010 - 4:20:41 PM

### Identifiers

• HAL Id : hal-00022125, version 1

### Citation

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