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Necessary and sufficient condition for M2-convergence to a Lévy process for billiards with cusps at flat points
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Jung, Paul, Melbourne, Ian, Pene, Francoise, Varandas, Paulo and Zhang, Hong-Kun (2021) Necessary and sufficient condition for M2-convergence to a Lévy process for billiards with cusps at flat points. Stochastics and Dynamics, 21 (5). 2150024. doi:10.1142/S0219493721500246 ISSN 0219-4937.
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Official URL: https://doi.org/10.1142/S0219493721500246
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 M1 and M2 Skorohod topologies has been studied in recent work. Here, we show that certain sufficient conditions for M2-convergence are also necessary.
| Item Type: | Journal Article | ||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
| Library of Congress Subject Headings (LCSH): | Lévy processes , Brownian motion processes, Stochastic processes , Convergence | ||||||||
| Journal or Publication Title: | Stochastics and Dynamics | ||||||||
| Publisher: | World Scientific Publishing Co. Pte. Ltd. | ||||||||
| ISSN: | 0219-4937 | ||||||||
| Official Date: | August 2021 | ||||||||
| Dates: |
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| Volume: | 21 | ||||||||
| Number: | 5 | ||||||||
| Article Number: | 2150024 | ||||||||
| DOI: | 10.1142/S0219493721500246 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Reuse Statement (publisher, data, author rights): | Electronic version of an article published as Stochastics and Dynamics, Volume, Issue, 2021 Pages] https://doi.org/10.1142/S0219493721500246 © copyright World Scientific Publishing Company https://www.worldscientific.com/worldscinet/sd | ||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||
| Date of first compliant deposit: | 31 July 2020 | ||||||||
| Date of first compliant Open Access: | 4 September 2021 | ||||||||
| RIOXX Funder/Project Grant: |
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