Extreme value theory for non-uniformly expanding dynamical systems

Holland, Mark; Nicol, Matthew; Török, Andrei

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

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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