Entry time statistics to different shrinking sets

Abstract

We consider $\psi$-mixing dynamical systems $(\mathcal{X},T,B,\mu )$ and we find conditions on families of sets $\{{\mathcal{U}}_n\subset \mathcal{X}:n\in \mathbb{N}\}$ so that $\mu ({\mathcal{U}}_n){\tau }_n$ tends in law to an exponential random variable, where ${\tau }_n$ is the entry time to ${\mathcal{U}}_n.$

References in corpus (1)

• Note on limit distribution of normalized return times and escape rate