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An invariance principle for weakly dependent stationary general models

Paul Doukhan·Olivier Wintenberger
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Abstract

The aim of this article is to refine a weak invariance principle for stationary sequences given by Doukhan & Louhichi (1999). Since our conditions are not causal our assumptions need to be stronger than the mixing and causal $θ$-weak dependence assumptions used in Dedecker & Doukhan (2003). Here, if moments of order $>2$ exist, a weak invariance principle and convergence rates in the CLT are obtained; Doukhan & Louhichi (1999) assumed the existence of moments with order $>4$. Besides the previously used $η$- and $κ$-weak dependence conditions, we introduce a weaker one, $λ$, which fits the Bernoulli shifts with dependent inputs.

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Paul Doukhan, Olivier Wintenberger. 2007-09-19. An invariance principle for weakly dependent stationary general models. https://arxiv.org/abs/math/0603221

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