Extreme value theory for non-uniformly expanding dynamical systems

Holland, Mark; Nicol, Matthew; Török, Andrei

doi:10.1090/S0002-9947-2011-05271-2

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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
Posted: 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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