The Dynkin-Lamperti arc-sine laws for measure preserving transformations

DOI10.1090/S0002-9947-98-02312-5zbMath0910.28014OpenAlexW1527385149MaRDI QIDQ4211161

Maximilian Thaler

Publication date: 10 September 1998

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-98-02312-5

zbMATH Keywords

renewal theoryinfinite ergodic theoryarc-sine law

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Measure-preserving transformations (28D05) Renewal theory (60K05)

Related Items

Distributional limit theorems in infinite ergodic theory ⋮ Mixing rates for intermittent maps of high exponent ⋮ Measure preserving transformations similar to Markov shifts ⋮ A functional stable limit theorem for Gibbs-Markov maps ⋮ Limit theory for some positive stationary processes with infinite mean ⋮ Operator renewal theory and mixing rates for dynamical systems with infinite measure ⋮ Return- and hitting-time limits for rare events of null-recurrent Markov maps ⋮ Infinite measure preserving transformations with compact first regeneration ⋮ ASYMPTOTIC DISTRIBUTIONS AND LARGE DEVIATIONS FOR ITERATED MAPS WITH AN INDIFFERENT FIXED POINT ⋮ Return- and hitting-time distributions of small sets in infinite measure preserving systems ⋮ Generalized arcsine law and stable law in an infinite measure dynamical system ⋮ Mixing limit theorems for ergodic transformations ⋮ Measure preserving extensions and minimal wandering rates ⋮ Functional limit theorem for occupation time processes of intermittent maps ⋮ A Fréchet law and an Erdős–Philipp law for maximal cuspidal windings ⋮ Improved mixing rates for infinite measure-preserving systems ⋮ LIMIT LAWS FOR DISTORTED CRITICAL RETURN TIME PROCESSES IN INFINITE ERGODIC THEORY ⋮ Distributional behavior of time averages of non-\(L^1\) observables in one-dimensional intermittent maps with infinite invariant measures

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Transformations on [0,1 with infinite invariant measures]
• Random f-expansions
• Estimates of the invariant densities of endomorphisms with indifferent fixed points
• The asymptotic distributional behaviour of transformations preserving infinite measures
• The invariant densities for maps modeling intermittency.
• A limit theorem for the Perron-Frobenius operator of transformations on [0,1 with indifferent fixed points]
• On Occupation Times for Markoff Processes
• An Occupation Time Theorem for A Class of Stochastic Processes
• Further notes on branching processes with mean 1