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http://bura.brunel.ac.uk/handle/2438/27864| Title: | Expansions in the Local and the Central Limit Theorems for Dynamical Systems |
| Authors: | Fernando, K Pène, F |
| Issue Date: | 11-Nov-2021 |
| Publisher: | Springer Nature |
| Citation: | Fernando, K. and Pène, F. (2021) 'Expansions in the Local and the Central Limit Theorems for Dynamical Systems', Communications in Mathematical Physics, 389 (1), pp. 273 - 347. doi: 10.1007/s00220-021-04255-z. |
| Abstract: | We study higher order expansions both in the Berry–Esséen estimate (Edgeworth expansions) and in the local limit theorems for Birkhoff sums of chaotic probability preserving dynamical systems. We establish general results under technical assumptions, discuss the verification of these assumptions and illustrate our results by different examples (subshifts of finite type, Young towers, Sinai billiards, random matrix products), including situations of unbounded observables with integrability order arbitrarily close to the optimal moment condition required in the i.i.d. setting. |
| Description: | The preprint on this institutional repository is available on arXiv at: arXiv:2008.08726v1 [math.DS] (https://doi.org/10.48550/arXiv.2008.08726). It has not been certified by peer review. You are advised to refer to the peer reviewed, authoritative version of record at https://doi.org/10.1007/s00220-021-04255-z . |
| URI: | https://bura.brunel.ac.uk/handle/2438/27864 |
| DOI: | https://doi.org/10.1007/s00220-021-04255-z |
| ISSN: | 0010-3616 |
| Other Identifiers: | ORCID iD: Kasun Fernando https://orcid.org/0000-0003-1489-9566 |
| Appears in Collections: | Dept of Mathematics Research Papers |
Files in This Item:
| File | Description | Size | Format | |
|---|---|---|---|---|
| Preprint.pdf | The preprint on this institutional repository is available on arXiv at: arXiv:2008.08726v1 [math.DS] (https://doi.org/10.48550/arXiv.2008.08726). It has not been certified by peer review. You are advised to refer to the peer reviewed, authoritative version of record at https://doi.org/10.1007/s00220-021-04255-z . | 769.45 kB | Adobe PDF | View/Open |
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