An improvement of the mixing rates in a counter-example to the weak invariance principle

Davide Giraudo (1)

1 LMRS - Laboratoire de Mathématiques Raphaël Salem

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 $q < 1$.

Domaines: Probabilités [math.PR]

Davide Giraudo. An improvement of the mixing rates in a counter-example to the weak invariance principle. 2015. ⟨hal-01114898⟩