The compound Poisson distribution and return times in dynamical systems

DOI10.1007/s00440-008-0153-yzbMath1175.37014arXiv0804.1032OpenAlexW2067601052MaRDI QIDQ2391169

Sandro Vaienti, Nicolai T. A. Haydn

Publication date: 24 July 2009

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0804.1032

zbMATH Keywords

periodic pointsmixing dynamical systemcompound Poisson distributionreturn times

Mathematics Subject Classification ID

Dynamical systems and their relations with probability theory and stochastic processes (37A50) Approximations to statistical distributions (nonasymptotic) (62E17)

Related Items (33)

The compound Poisson limit ruling periodic extreme behaviour of non-uniformly hyperbolic dynamics ⋮ Extreme value theory for synchronization of coupled map lattices ⋮ Rare events for the Manneville-Pomeau map ⋮ Extremal dichotomy for uniformly hyperbolic systems ⋮ On some compound random variables motivated by bulk queues ⋮ Nonconventional Poisson limit theorems ⋮ Extreme value laws for dynamical systems with countable extremal sets ⋮ Laws of rare events for deterministic and random dynamical systems ⋮ Return times at periodic points in random dynamics ⋮ Compound Poisson law for hitting times to periodic orbits in two-dimensional hyperbolic systems ⋮ Cluster distributions for dynamically defined point processes ⋮ Spatio-temporal Poisson processes for visits to small sets ⋮ Extreme value distributions of observation recurrences ⋮ Poisson and compound Poisson approximations in conventional and nonconventional setups ⋮ Inference for Type II bivariate Pólya–Aeppli distribution ⋮ Extremal behaviour of chaotic dynamics ⋮ Entry and return times distribution ⋮ On a Bivariate Pólya-Aeppli Distribution ⋮ Hitting time statistics and extreme value theory ⋮ Generalized Fibonacci numbers and extreme value laws for the Rényi map ⋮ The extremal index, hitting time statistics and periodicity ⋮ Complete convergence and records for dynamically generated stochastic processes ⋮ Rare event process and entry times distribution for arbitrary null sets on compact manifolds ⋮ Escape rate and conditional escape rate from a probabilistic point of view ⋮ Local escape rates for -mixing dynamical systems ⋮ Compound Poisson statistics for multiple returns in shrinking cylinders for mixing processes ⋮ A Poisson limit theorem for Gibbs–Markov maps ⋮ Limiting entry and return times distribution for arbitrary null sets ⋮ On the computation of the extremal index for time series ⋮ Extreme value theory for non-uniformly expanding dynamical systems ⋮ Application of the Convergence of the Spatio-Temporal Processes for Visits to Small Sets ⋮ Poisson approximations and convergence rates for hyperbolic dynamical systems ⋮ Clustering of extreme events created by multiple correlated maxima

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