Return-Time Statistics, Hitting-Time Statistics and Inducing

DOI10.1007/978-1-4939-0419-8_10zbMath1352.37002OpenAlexW117431011MaRDI QIDQ5259678

Roland Zweimüller, Nicolai T. A. Haydn, Nicole Winterberg

Publication date: 29 June 2015

Published in: Springer Proceedings in Mathematics & Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-1-4939-0419-8_10

zbMATH Keywords

hitting-time statisticsreturn-time statisticsprobability-preserving transformations

Mathematics Subject Classification ID

Dynamical aspects of measure-preserving transformations (37A05) Ergodicity, mixing, rates of mixing (37A25) Dynamical systems and their relations with probability theory and stochastic processes (37A50) Notions of recurrence and recurrent behavior in topological dynamical systems (37B20)

Related Items (10)

The general asymptotic return-time process ⋮ Rare events for the Manneville-Pomeau map ⋮ Extreme value laws for dynamical systems with countable extremal sets ⋮ Hitting times and positions in rare events ⋮ Cluster distributions for dynamically defined point processes ⋮ Entry and return times for semi-flows ⋮ Return- and hitting-time limits for rare events of null-recurrent Markov maps ⋮ Hitting-time limits for some exceptional rare events of ergodic maps ⋮ Complete convergence and records for dynamically generated stochastic processes ⋮ Clustering of extreme events created by multiple correlated maxima

Cites Work

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• Asymptotics for hitting times
• Statistics of return times: A general framework and new applications
• Possible limit laws for entrance times of an ergodic aperiodic dynamical system.
• Mixing limit theorems for ergodic transformations
• Hitting and return times in ergodic dynamical systems
• Rare events, exponential hitting times and extremal indices via spectral perturbation†
• AN INTRODUCTION TO QUANTITATIVE POINCARÉ RECURRENCE IN DYNAMICAL SYSTEMS
• Return time statistics via inducing
• Invariant measures for general(ized) induced transformations
• Return time statistics for unimodal maps

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