large deviations estimates
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2019 ◽  
Vol 20 (05) ◽  
pp. 2050030
Author(s):  
Matthew Nicol ◽  
Andrew Török

We consider exponential large deviations estimates for unbounded observables on uniformly expanding dynamical systems. We show that uniform expansion does not imply the existence of a rate function for unbounded observables no matter the tail behavior of the cumulative distribution function. We give examples of unbounded observables with exponential decay of autocorrelations, exponential decay under the transfer operator in each [Formula: see text], [Formula: see text], and strictly stretched exponential large deviation. For observables of form [Formula: see text], [Formula: see text] periodic, on uniformly expanding systems we give the precise stretched exponential decay rate. We also show that a classical example in the literature of a bounded observable with exponential decay of autocorrelations yet with no rate function is degenerate as the observable is a coboundary.


2018 ◽  
Vol 18 (03) ◽  
pp. 1850018
Author(s):  
Yuri Kifer

We extend the Erdős–Rényi law of large numbers to the averaging setup both in discrete and continuous time cases. We consider both stochastic processes and dynamical systems as fast motions whenever they are fast mixing and satisfy large deviations estimates. In the continuous time case we consider flows with large deviations estimates which allow a suspension representation and it turns out that fast mixing of corresponding base transformations suffices for our results.


2018 ◽  
Vol 24 (2) ◽  
pp. 605-637 ◽  
Author(s):  
Daria Ghilli

We study singular perturbation problems for second order HJB equations in an unbounded setting. The main applications are large deviations estimates for the short maturity asymptotics of stochastic systems affected by a stochastic volatility, where the volatility is modelled by a process evolving at a faster time scale and satisfying some condition implying ergodicity.


2014 ◽  
Vol 8 (4) ◽  
Author(s):  
Sonia Chaari ◽  
Achref Majid ◽  
Habib Ouerdiane

2012 ◽  
Vol 391 (22) ◽  
pp. 5658-5671 ◽  
Author(s):  
Patrick Loiseau ◽  
Claire Médigue ◽  
Paulo Gonçalves ◽  
Najmeddine Attia ◽  
Stéphane Seuret ◽  
...  

2009 ◽  
Vol 71 (11) ◽  
pp. 5572-5586 ◽  
Author(s):  
C. Brändle ◽  
E. Chasseigne

2008 ◽  
Vol DMTCS Proceedings vol. AI,... (Proceedings) ◽  
Author(s):  
Nicolas Broutin ◽  
Philippe Flajolet

International audience This extended abstract is dedicated to the analysis of the height of non-plane unlabelled rooted binary trees. The height of such a tree chosen uniformly among those of size $n$ is proved to have a limiting theta distribution, both in a central and local sense. Moderate as well as large deviations estimates are also derived. The proofs rely on the analysis (in the complex plane) of generating functions associated with trees of bounded height.


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