Convergence to a Lévy process in the Skorohod \(\mathcal{M}_1\) and \(\mathcal{M}_2\) topologies for nonuniformly hyperbolic systems, including billiards with cusps
DOI10.1007/s00220-019-03501-9zbMath1440.37013arXiv1809.06572OpenAlexW3092391370MaRDI QIDQ1986583
Publication date: 8 April 2020
Published in: Communications in Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1809.06572
Processes with independent increments; Lévy processes (60G51) Dynamical systems and their relations with probability theory and stochastic processes (37A50) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25) Dynamical systems with singularities (billiards, etc.) (37C83)
Related Items (6)
Cites Work
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- Characterization of weak convergence of Birkhoff sums for Gibbs-Markov maps
- Limit theorems for dispersing billiards with cusps
- A functional limit theorem for dependent sequences with infinite variance stable limits
- Almost sure invariance principle for nonuniformly hyperbolic systems
- Limit theorems in the stadium billiard
- Dispersing billiards with cusps: slow decay of correlations
- Chaotic advection in a two-dimensional flow: Lévy flights and anomalous diffusion
- Statistical properties of Lorentz gas with periodic configuration of scatterers
- 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
- Stable laws for chaotic billiards with cusps at flat points
- Statistical limit theorems for suspension flows
- Decay of correlations and dispersing billiards.
- A limit theorem for the Perron-Frobenius operator of transformations on [0,1 with indifferent fixed points]
- An expansion estimate for dispersing planar billiards with corner points
- Weak convergence to stable Lévy processes for nonuniformly hyperbolic dynamical systems
- A limit theorem for moving averages in the \(\alpha\)-stable domain of attraction
- Mixing limit theorems for ergodic transformations
- Stochastic-Process Limits
- Statistical properties of a skew product with a curve of neutral points
- WEAK CONVERGENCE TO LÉVY STABLE PROCESSES IN DYNAMICAL SYSTEMS
- Sporadicity: Between periodic and chaotic dynamical behaviors
- Some Simple Conditions for Limit Theorems to Be Mixing
- Ergodic structure and invariant densities of non-Markovian interval maps with indifferent fixed points
- A probabilistic approach to intermittency
- Decay of correlations in one-dimensional dynamics
- LOCAL LIMIT THEOREMS FOR PARTIAL SUMS OF STATIONARY SEQUENCES GENERATED BY GIBBS–MARKOV MAPS
- Billiards with polynomial decay of correlations
- Upper and lower bounds for the correlation function via inducing with general return times
- Decay of correlations for billiards with flat points II: cusps effect
- Necessary and sufficient condition for ℳ2-convergence to a Lévy process for billiards with cusps at flat points
- Convergence to a-stable Lévy motion for chaotic billiards with several cusps at flat points
- Billiards with polynomial mixing rates
- A FAMILY OF CHAOTIC BILLIARDS WITH VARIABLE MIXING RATES
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