Escape rate and conditional escape rate from a probabilistic point of view

Abstract

We prove that for a sequence of nested sets $\{U_n\}$ with $\Lambda ={\cap }_n{U}_n$ a measure zero set, the localized escape rate converges to the extremal index of $\Lambda$, provided that the dynamical system is $\varphi$-mixing at polynomial speed. We also establish the general equivalence between the local escape rate for entry times and the local escape rate for returns.

References in corpus (1)

• Limiting entry times distribution for arbitrary null sets SETS

Cited by in corpus (1)

• A functional limit theorem for a dynamical system with an observable maximised on a Cantor set