Extreme value theory for non-uniformly expanding dynamical systems

By Mark Holland, Matthew Nicol, Andrei Török. 2012

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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.

Subfields: Economics and Econometrics, Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7a75913d8ca8ddde4acc3e90a8b5467e8c1d92b6