In [1], the authors gave an example of absolutely regular strictly stationary process that satisfies the central limit theorem, but not the weak invariance principle. For each , the process can be constructed with mixing rates of order . The goal of this note is to show that actually the same construction can give mixing rates of order for a given .
Dans [1], les auteurs ont fourni un exemple de processus strictement stationnaire β-mélangeant vérifiant le théorème limite central, mais pas le principe d'invariance faible. Pour tout , le processus peut être construit avec des taux de mélange de l'ordre de . L'objectif de cette note est de montrer que la même construction peut fournir des taux de mélange de l'ordre de pour un donné.
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Davide Giraudo 1
@article{CRMATH_2015__353_10_953_0, author = {Davide Giraudo}, title = {An improvement of the mixing rates in a counter-example to the weak invariance principle}, journal = {Comptes Rendus. Math\'ematique}, pages = {953--958}, publisher = {Elsevier}, volume = {353}, number = {10}, year = {2015}, doi = {10.1016/j.crma.2015.07.013}, language = {en}, }
Davide Giraudo. An improvement of the mixing rates in a counter-example to the weak invariance principle. Comptes Rendus. Mathématique, Volume 353 (2015) no. 10, pp. 953-958. doi : 10.1016/j.crma.2015.07.013. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.07.013/
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