Article ID Journal Published Year Pages File Type
1155383 Stochastic Processes and their Applications 2016 26 Pages PDF
Abstract

Suppose (f,X,ν)(f,X,ν) is a measure preserving dynamical system and ϕ:X→Rϕ:X→R is an observable with some degree of regularity. We investigate the maximum process Mn:=max(X1,…,Xn)Mn:=max(X1,…,Xn), where Xi=ϕ∘fiXi=ϕ∘fi is a time series of observations on the system. When Mn→∞Mn→∞ almost surely, we establish results on the almost sure growth rate, namely the existence (or otherwise) of a sequence un→∞un→∞ such that Mn/un→1Mn/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.

Related Topics
Physical Sciences and Engineering Mathematics Mathematics (General)
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