An improvement of the mixing rates in a counter-example to the weak invariance principle
Résumé
In [1], the authors gave an example of absolutely regular strictly stationary process which satisfies the central limit theorem but not the weak invariance principle. For each $q < /1/2$, the process can be constructed with mixing rates of order $N^{−q}$ . The goal of this note is to show that actually the same construction can give mixing rates of order $N^{ −q}$ for a given $q < 1$.
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Requiert hal-00911758 Article Davide Giraudo, Dalibor Volný. A strictly stationary $\beta$-mixing process satisfying the central limit theorem but not the weak invariance principle. Stochastic Processes and their Applications, 2014, 124, pp.3769-3781. ⟨10.1016/j.spa.2014.06.008⟩. ⟨hal-00911758v2⟩