Necessary and sufficient condition for ℳ2-convergence to a Lévy process for billiards with cusps at flat points

DOI10.1142/S0219493721500246zbMath1481.37006arXiv1902.08958OpenAlexW3083222407MaRDI QIDQ5157731

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Publication date: 20 October 2021

Published in: Stochastics and Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1902.08958

zbMATH Keywords

Lévy processesanomalous diffusionSkorohod topologybilliards with flat cusps

Mathematics Subject Classification ID

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) Dynamical systems with singularities (billiards, etc.) (37C83)

Related Items (2)

Cusps in heavy billiards ⋮ Convergence to a Lévy process in the Skorohod \(\mathcal{M}_1\) and \(\mathcal{M}_2\) topologies for nonuniformly hyperbolic systems, including billiards with cusps

Cites Work

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• Limit theorems for dispersing billiards with cusps
• Stable laws for chaotic billiards with cusps at flat points
• Convergence to a Lévy process in the Skorohod \(\mathcal{M}_1\) and \(\mathcal{M}_2\) topologies for nonuniformly hyperbolic systems, including billiards with cusps
• Weak convergence to stable Lévy processes for nonuniformly hyperbolic dynamical systems
• Stochastic-Process Limits
• Some Useful Functions for Functional Limit Theorems
• Decay of correlations for billiards with flat points II: cusps effect
• Convergence to a-stable Lévy motion for chaotic billiards with several cusps at flat points

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