The Library
Convergence to a Lévy process in the Skorohod M1 and M2 topologies for nonuniformly hyperbolic systems, including billiards with cusps
Tools
Tools
Tools
Melbourne, Ian and Varandas, Paulo (2020) Convergence to a Lévy process in the Skorohod M1 and M2 topologies for nonuniformly hyperbolic systems, including billiards with cusps. Communications in Mathematical Physics, 375 . pp. 653-678. doi:10.1007/s00220-019-03501-9 ISSN 0010-3616.
|
PDF
WRAP-convergence-Levy-process-Skorohod-M1-M2-topologies-nonuniformly-hyperbolic-systems-Melbourne-2019.pdf - Accepted Version - Requires a PDF viewer. Download (787Kb) | Preview |
Official URL: https://doi.org/10.1007/s00220-019-03501-9
Abstract
We prove convergence to a Lévy process for a class of dispersing billiards with cusps. For such examples, convergence to a stable law was proved by Jung & Zhang. For the corresponding functional limit law, convergence is not possible in the usual Skorohod J1 topology. Our main results yield elementary geometric conditions for convergence (i) in M1, (ii) in M2 but not M1. In general, we show for a large class of nonuniformly hyperbolic systems how to deduce functional limit laws once convergence to the corresponding stable law is known.
| Item Type: | Journal Article | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | |||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | |||||||||
| Library of Congress Subject Headings (LCSH): | Lévy processes, Limit theorems (Probability theory) | |||||||||
| Journal or Publication Title: | Communications in Mathematical Physics | |||||||||
| Publisher: | Springer | |||||||||
| ISSN: | 0010-3616 | |||||||||
| Official Date: | April 2020 | |||||||||
| Dates: |
|
|||||||||
| Volume: | 375 | |||||||||
| Page Range: | pp. 653-678 | |||||||||
| DOI: | 10.1007/s00220-019-03501-9 | |||||||||
| Status: | Peer Reviewed | |||||||||
| Publication Status: | Published | |||||||||
| Reuse Statement (publisher, data, author rights): | This is a post-peer-review, pre-copyedit version of an article published in Communications in Mathematical Physics. The final authenticated version is available online at: http://dx.doi.org/10.1007/s00220-019-03501-9 | |||||||||
| Access rights to Published version: | Restricted or Subscription Access | |||||||||
| Date of first compliant deposit: | 22 May 2019 | |||||||||
| Date of first compliant Open Access: | 29 June 2020 | |||||||||
| RIOXX Funder/Project Grant: |
|
|||||||||
| Related URLs: |
Request changes or add full text files to a record
Repository staff actions (login required)
 |
View Item |
Downloads
Downloads per month over past year
