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H 2 ​​​Growth of normalizing sequences in limit theorems

Auteurs : Gouëzel, Sébastien (Auteur de la Conférence)
CIRM (Editeur )

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​limit theorems in ergodic theory examples of limit theorems in ergodic theory normalizing sequences in probability-preserving maps infinite ergodic theory normalizing sequences in infinite measure limit theorems in renewal Markov chains renewal theorem proof assistants for mathematical research Isabelle/HOL questions from the audience

Résumé : ​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 $1$.

Codes MSC :
60F05 - Central limit and other weak theorems
37A40 - Nonsingular (and infinite-measure preserving) transformations

    Informations sur la Vidéo

    Langue : Anglais
    Date de publication : 15/11/2018
    Date de captation : 31/10/2018
    Collection : Research talks
    Format : MP4 (.mp4) - HD
    Durée : 00:54:32
    Domaine : Probability & Statistics ; Dynamical Systems & ODE
    Audience : Chercheurs ; Doctorants , Post - Doctorants
    Download : https://videos.cirm-math.fr/2018-10-31_Gouezel.mp4

Informations sur la rencontre

Nom de la rencontre : Probabilistic limit theorems for dynamical systems / Théorèmes limites probabilistes pour les systèmes dynamiques
Organisateurs de la rencontre : Melbourne, Ian ; Pène, Françoise ; Volny, Dalibor
Dates : 29/10/2018 - 02/11/2018
Année de la rencontre : 2018
URL Congrès : https://conferences.cirm-math.fr/1997.html

Citation Data

DOI : 10.24350/CIRM.V.19471103
Cite 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

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