AN INVARIANCE PRINCIPLE FOR WEAKLY DEPENDENT STATIONARY
GENERAL MODELS
Paul Doukhan
Olivier Wintenberger
Abstract: The aim of this paper is to refine a weak invariance principle for stationary
sequences given by Doukhan and Louhichi [10]. Since our conditions are not causal, our
assumptions need to be stronger than the mixing and causal -weak dependence
assumptions used in Dedecker and Doukhan [5]. Here, if moments of order greater than
exist, a weak invariance principle and convergence rates in the CLT are obtained;
Doukhan and Louhichi [10] assumed the existence of moments with order greater
than Besides the - and -weak dependence conditions used previously, we
introduce a weaker one, which fits the Bernoulli shifts with dependent inputs.
2000 AMS Mathematics Subject Classification: Primary: 60F17.
Key words and phrases: Invariance principle, weak dependence, the Bernoulli shifts.