Mixing limit theorems for ergodic transformations
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Publication:2471125
DOI10.1007/s10959-007-0085-yzbMath1137.60017OpenAlexW2040159604MaRDI QIDQ2471125
Publication date: 18 February 2008
Published in: Journal of Theoretical Probability (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10959-007-0085-y
Weak invariance principleHitting timesErgodic transformationsFunctional limit theoremMean ergodic theoremMixing limit theoremStrong distributional convergence
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Cites Work
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- Distributional limit theorems in infinite ergodic theory
- Ergodic theorems. With a supplement by Antoine Brunel
- Random f-expansions
- The asymptotic distributional behaviour of transformations preserving infinite measures
- On mixing and stability of limit theorems
- Statistical limit theorems for suspension flows
- Asymptotics for hitting times
- Statistics of return times: A general framework and new applications
- On almost-sure versions of classical limit theorems for dynamical systems
- Statistics of close visits to the indifferent fixed point of an interval map
- On mixing sequences of sets
- An Invariance Principle in Renewal Theory
- Some Simple Conditions for Limit Theorems to Be Mixing
- The Dynkin-Lamperti arc-sine laws for measure preserving transformations
- Poisson law for Axiom A diffeomorphisms
- Mixing for Markov operators
- Mean ergodic theorem in Banach spaces
- The Influence of the Maximum Term in the Addition of Independent Random Variables
- Convergence of stochastic processes
- Non exponential law of entrance times in asymptotically rare events for intermittent maps with infinite invariant measure
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