Speed of convergence for laws of rare events and escape rates
Abstract
We obtain error terms on the rate of convergence to Extreme Value Laws, and to the asymptotic Hitting Time Statistics, for a general class of weakly dependent stochastic processes. The dependence of the error terms on the ‘time’ and ‘length’ scales is very explicit. Specialising to data derived from a class of dynamical systems we find even more detailed error terms, one application of which is to consider escape rates through small holes in these systems.
Citation
Freitas , A , Freitas , J & Todd , M J 2015 , ' Speed of convergence for laws of rare events and escape rates ' Stochastic Processes and their Applications , vol. 125 , no. 4 , pp. 1653-1687 . DOI: 10.1016/j.spa.2014.11.011
Publication
Stochastic Processes and their Applications
Status
Peer reviewed
ISSN
1879-209XType
Journal article
Rights
Copyright 2014 Elsevier B.V. All rights reserved. This is the author’s version of a work that was accepted for publication in Stochastic Processes and their Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Stochastic Processes and their Applications, 125, 4, April 2015 DOI 10.1016/j.spa.2014.11.011
Description
MT was partially supported by NSF grant DMS 1109587. All authors are supported by FCT (Portugal) projects PTDC/MAT/099493/2008 and PTDC/MAT/120346/2010, which are financed by national and European structural funds through the programs FEDER and COMPETE. All three authors were also supported by CMUP, which is financed by FCT (Portugal) through the programs POCTI and POSI, with national and European structural funds, under the project PEst-C/MAT/UI0144/2013.Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.