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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Extreme value theory for non-uniformly expanding dynamical systems


Authors: Mark Holland, Matthew Nicol and Andrei Török
Journal: Trans. Amer. Math. Soc. 364 (2012), 661-688
MSC (2010): Primary 37D99; Secondary 60F99
Published electronically: October 4, 2011
MathSciNet review: 2846347
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Abstract: We establish extreme value statistics for functions with multiple maxima and some degree of regularity on certain non-uniformly expanding dynamical systems. We also establish extreme value statistics for time series of observations on discrete and continuous suspensions of certain non-uniformly expanding dynamical systems via a general lifting theorem. The main result is that a broad class of observations on these systems exhibit the same extreme value statistics as i.i.d. processes with the same distribution function.


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Additional Information

Mark Holland
Affiliation: School of Engineering, Computer Science and Mathematics, University of Exeter, North Park Road, Exeter, EX4 4QF, England
Email: m.p.holland@exeter.ac.uk

Matthew Nicol
Affiliation: Department of Mathematics, University of Houston, Houston, Texas 77204-3008
Email: nicol@math.uh.edu

Andrei Török
Affiliation: Department of Mathematics, University of Houston, Houston, Texas 77204-3008
Email: torok@math.uh.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-2011-05271-2
PII: S 0002-9947(2011)05271-2
Received by editor(s): February 12, 2009
Received by editor(s) in revised form: December 1, 2009
Published electronically: October 4, 2011
Additional Notes: The research of the second and third authors was supported in part by the National Science Foundation grants DMS-0607345 and DMS-0600927. We thank Henk Bruin for useful discussions, especially in connection with Lemma 3.10. We also wish to thank an anonymous referee for helpful suggestions and in particular the proof of Lemma 4.16.
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.