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Growth of normalizing sequences in limit theorems
Post-edited
Authors : Gouëzel, Sébastien (Author of the conference)
CIRM (Publisher )
60F05 - Central limit and other weak theorems
37A40 - Nonsingular (and infinite-measure preserving) transformations
CIRM (Publisher )
Abstract :
Assume that a renormalized Birkhoff sum $S_n f/B_n$ converges in distribution to a nontrivial limit. What can one say about the sequence $B_n$? Most natural statements in the literature involve sequences $B_n$ of the form $B_n = n^\alpha L(n)$, where $L$ is slowly varying. We will discuss the possible growth rate of $B_n$ both in the probability preserving case and the conservative case. In particular, we will describe examples where $B_n$ grows superpolynomially, or where $B_{n+1}/B_n$ does not tend to $1$.
MSC Codes : 60F05 - Central limit and other weak theorems
37A40 - Nonsingular (and infinite-measure preserving) transformations
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 15/11/2018 Conference Date : 31/10/2018 Subseries : Research talks arXiv category : Dynamical Systems Mathematical Area(s) : Probability & Statistics ; Dynamical Systems & ODE Format : MP4 (.mp4) - HD Video Time : 00:54:32 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2018-10-31_Gouezel.mp4 
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Information on the Event
Event Title : Probabilistic limit theorems for dynamical systems / Théorèmes limites probabilistes pour les systèmes dynamiquesEvent Organizers : Melbourne, Ian ; Pène, Françoise ; Volny, Dalibor Dates : 29/10/2018 - 02/11/2018 Event Year : 2018 Event URL : https://conferences.cirm-math.fr/1997.html
Citation Data
DOI : 10.24350/CIRM.V.19471103Cite this video as: Gouëzel, Sébastien (2018). Growth of normalizing sequences in limit theorems. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19471103 URI : http://dx.doi.org/10.24350/CIRM.V.19471103 |
See Also
- [Multi angle] Mixing and the local central limit theorem for hyperbolic dynamical systems / Author of the conference Nándori, Péter.
- [Multi angle] Levy diffusion of dispersing billiards with flat points / Author of the conference Zhang, Hong-Kun.
- [Multi angle] Diffusion limit for a slow-fast standard map / Author of the conference De Simoi, Jacopo.
- [Multi angle] Limit theorems for almost Anosov flows / Author of the conference Terhesiu, Dalia.
Bibliography
- Gouëzel, S. (2018). Growth of normalizing sequences in limit theorems for conservative maps.
