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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Extreme value theory for non-uniformly expanding dynamical systems
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by Mark Holland, Matthew Nicol and Andrei Török PDF
Trans. Amer. Math. Soc. 364 (2012), 661-688 Request permission

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
  • MR Author ID: 350236
  • Email: nicol@math.uh.edu
  • Andrei Török
  • Affiliation: Department of Mathematics, University of Houston, Houston, Texas 77204-3008
  • MR Author ID: 249702
  • Email: torok@math.uh.edu
  • 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.
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 364 (2012), 661-688
  • MSC (2010): Primary 37D99; Secondary 60F99
  • DOI: https://doi.org/10.1090/S0002-9947-2011-05271-2
  • MathSciNet review: 2846347