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An invariance principle for weakly dependent stationary general models. (English) Zbl 1124.60031

Summary: The aim of this paper is to refine a weak invariance principle for stationary sequences given by P. Doukhan and S. Louhichi [Stochastic Processes Appl. 84, No. 2, 313–342 (1999; Zbl 0996.60020)]. Since our conditions are not causal, our assumptions need to be stronger than the mixing and causal \(\theta\)-weak dependence assumptions used by J. Dedecker and P. Doukhan [Stochastic Processes Appl. 106, No. 1, 63–80 (2003; Zbl 1075.60513)]. Here, if moments of order greater than 2 exist, a weak invariance principle and convergence rates in the CLT are obtained; Doukhan and Louhichi [loc. cit.] assumed the existence of moments with order greater than 4. Besides the \(\eta\)- and \(\kappa\)-weak dependence conditions used previously, we introduce a weaker one, \(\lambda\), which fits the Bernoulli shifts with dependent inputs.

MSC:

60F17 Functional limit theorems; invariance principles
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