Speed of convergence for laws of rare events and escape rates

Ana Freitas; Jorge Freitas; Michael John Todd

doi:10.1016/j.spa.2014.11.011

Speed of convergence for laws of rare events and escape rates

Ana Freitas, Jorge Freitas, Michael John Todd

Pure Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	1653-1687
Number of pages	35
Journal	Stochastic Processes and their Applications
Volume	125
Issue number	4
Early online date	24 Nov 2014
DOIs	https://doi.org/10.1016/j.spa.2014.11.011
Publication status	Published - Apr 2015

Keywords

Extreme value theory
Return time statistics
Stationary stochastic processes
Metastability

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10.1016/j.spa.2014.11.011

ErrorTermsFFTfinal
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
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Cite this

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title = "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 {\textquoteleft}time{\textquoteright} and {\textquoteleft}length{\textquoteright} 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.",

keywords = "Extreme value theory, Return time statistics, Stationary stochastic processes, Metastability",

author = "Ana Freitas and Jorge Freitas and Todd, {Michael John}",

note = "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. ",

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T1 - Speed of convergence for laws of rare events and escape rates

AU - Freitas, Ana

AU - Freitas, Jorge

AU - Todd, Michael John

N1 - 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.

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N2 - 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.

AB - 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.

KW - Extreme value theory

KW - Return time statistics

KW - Stationary stochastic processes

KW - Metastability

U2 - 10.1016/j.spa.2014.11.011

DO - 10.1016/j.spa.2014.11.011

M3 - Article

SN - 1879-209X

VL - 125

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EP - 1687

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 4

ER -

Speed of convergence for laws of rare events and escape rates

Abstract

Keywords

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