Escape rate and conditional escape rate from a probabilistic point of view
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 \(\phi\)-mixing at polynomial speed. We also establish the general equivalence bet...
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| creator | Davis, Connor Nicolai Haydn Yang, Fan |
| description | 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 \(\phi\)-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. |
| doi_str_mv | 10.48550/arxiv.2006.06112 |
| format | Article |
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| subjects | Mathematics - Dynamical Systems Mathematics - Probability Polynomials |
| title | Escape rate and conditional escape rate from a probabilistic point of view |
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