Compound Poisson statistics for multiple returns in shrinking cylinders for mixing processes

DOI10.1017/ETDS.2014.139zbMath1381.37013OpenAlexW1982518868MaRDI QIDQ2828037

Ariel Rapaport

Publication date: 24 October 2016

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/etds.2014.139

zbMATH Keywords

Gibbs measurePólya-Aeppli distribution\(\psi\)-mixing

Mathematics Subject Classification ID

Discrete-time Markov processes on general state spaces (60J05) Ergodicity, mixing, rates of mixing (37A25) Dynamical systems and their relations with probability theory and stochastic processes (37A50) Thermodynamic formalism, variational principles, equilibrium states for dynamical systems (37D35) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55) Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. (37C30)

Related Items (1)

Spatio-temporal Poisson processes for visits to small sets

Cites Work

• Unnamed Item
• Nonconventional Poisson limit theorems
• Poisson and compound Poisson approximations in conventional and nonconventional setups
• The compound Poisson limit ruling periodic extreme behaviour of non-uniformly hyperbolic dynamics
• The compound Poisson distribution and return times in dynamical systems
• Sharp errors for point-wise Poisson approximations in mixing processes
• Poisson limit law for Markov chains
• Poisson law for Axiom A diffeomorphisms
• Mixing Properties and Central Limit Theorem for a Class of Non-Identical Piecewise Monotonic C ² - Transformations
• Equilibrium states and the ergodic theory of Anosov diffeomorphisms

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