Weak convergence to stable Lévy processes for nonuniformly hyperbolic dynamical systems
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Publication:2346184
DOI10.1214/13-AIHP586zbMath1380.37064arXiv1309.6429MaRDI QIDQ2346184
Roland Zweimüller, Ian Melbourne
Publication date: 29 May 2015
Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1309.6429
Measure-preserving transformations (28D05) Dynamical systems and their relations with probability theory and stochastic processes (37A50) Functional limit theorems; invariance principles (60F17) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25)
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Cites Work
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- Limit theorems for dispersing billiards with cusps
- Almost sure invariance principle for nonuniformly hyperbolic systems
- Limit theorems in the stadium billiard
- Almost sure invariance principle for dynamical systems by spectral methods
- Decay of correlations and invariance principles for dispersing billiards with cusps, and related planar billiard flows
- A vector-valued almost sure invariance principle for hyperbolic dynamical systems
- Ergodic properties of invariant measures for piecewise monotonic transformations
- Weak convergence of sums of moving averages in the \(\alpha\)-stable domain of attraction
- Distribution function inequalities for martingales
- Statistical properties of dynamical systems with some hyperbolicity
- Recurrence times and rates of mixing
- Central limit theorem and stable laws for intermittent maps
- Statistical limit theorems for suspension flows
- The central limit theorem for geodesic flows on \(n\)-dimensional manifolds of negative curvature
- Central limit theorems and invariance principles for time-one maps of hyperbolic flows
- Scaling limit for trap models on \(\mathbb Z^d\)
- Limit laws and recurrence for the planar Lorentz process with infinite horizon
- Mixing limit theorems for ergodic transformations
- Méthode de martingales et flot géodésique sur une surface de courbure constante négative
- Central limit theorems and suppression of anomalous diffusion for systems with symmetry
- Weak invariance principle and exponential bounds for some special functions of intermittent maps
- Approximation by Brownian motion for Gibbs measures and flows under a function
- Statistical properties of a skew product with a curve of neutral points
- WEAK CONVERGENCE TO LÉVY STABLE PROCESSES IN DYNAMICAL SYSTEMS
- Some Simple Conditions for Limit Theorems to Be Mixing
- A probabilistic approach to intermittency
- Decay of correlations, central limit theorems and approximation by Brownian motion for compact Lie group extensions
- LOCAL LIMIT THEOREMS FOR PARTIAL SUMS OF STATIONARY SEQUENCES GENERATED BY GIBBS–MARKOV MAPS
- STATISTICAL PROPERTIES OF ENDOMORPHISMS AND COMPACT GROUP EXTENSIONS
- STABLE LIMITS FOR PROBABILITY PRESERVING MAPS WITH INDIFFERENT FIXED POINTS
- Central limit theorems and invariance principles for Lorenz attractors
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