Necessary and sufficient condition for ℳ2-convergence to a Lévy process for billiards with cusps at flat points-Reference-Cited by-同舟云学术

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

Published:2020-09-04 Issue:05 Volume:21 Page:2150024
ISSN:0219-4937
Container-title:Stochastics and Dynamics
language:en
Short-container-title:Stoch. Dyn.

Author:

Jung Paul¹,Melbourne Ian²,Pène Françoise³,Varandas Paulo⁴,Zhang Hong-Kun⁵

Affiliation:

1. Department of Mathematical Sciences, KAIST, Daejeon, South Korea

2. Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK

3. Université de Brest, Institut Universitaire de France, LMBA, UMR CNRS 6205, 29238 Brest cedex, France

4. Departamento de Matemática, Universidade Federal da Bahia, 40170-110 Salvador, Brazil

5. Department of Mathematics, University of Massachusetts, Amherst, MA, USA

Abstract

We consider a class of planar dispersing billiards with a cusp at a point of vanishing curvature. Convergence to a stable law and to the corresponding Lévy process in the [Formula: see text] and [Formula: see text] Skorohod topologies has been studied in recent work. Here, we show that certain sufficient conditions for [Formula: see text]-convergence are also necessary.

Publisher

World Scientific Pub Co Pte Lt

Subject

Modelling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219493721500246

Reference10 articles.

1. Limit Theorems for Dispersing Billiards with Cusps

2. Convergence to a-stable Lévy motion for chaotic billiards with several cusps at flat points

3. Stable Laws for Chaotic Billiards with Cusps at Flat Points

4. Convergence to a Lévy Process in the Skorohod $${{\mathcal {M}}}_1$$ and $${{\mathcal {M}}}_2$$ Topologies for Nonuniformly Hyperbolic Systems, Including Billiards with Cusps

5. Weak convergence to stable Lévy processes for nonuniformly hyperbolic dynamical systems

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