Almost sure convergence of maxima for chaotic dynamical systems

M.P. Holland, M. Nicol and A. Török

Stochastic Processes and their Applications, 2016, vol. 126, issue 10, 3145-3170

Abstract: Suppose (f,X,ν) is a measure preserving dynamical system and ϕ:X→R is an observable with some degree of regularity. We investigate the maximum process Mn:=max(X1,…,Xn), where Xi=ϕ∘fi is a time series of observations on the system. When Mn→∞ almost surely, we establish results on the almost sure growth rate, namely the existence (or otherwise) of a sequence un→∞ such that Mn/un→1 almost surely. For a wide class of non-uniformly hyperbolic dynamical systems we determine where such an almost sure limit exists and give examples where it does not.

Keywords: Limit theorems for dynamical systems; Extreme value theory (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1016/j.spa.2016.04.023

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