A strictly stationary $\beta$-mixing process satisfying the central limit theorem but not the weak invariance principle

Davide Giraudo, Dalibor Volny

In 1983, N. Herrndorf proved that for a $\varphi$-mixing sequence satisfying the central limit theorem and ${\mathrm{liminf}}_{n\to \infty }\frac{{\sigma }_n^2}{n}>0$, the weak invariance principle takes plac…