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Weak convergence to extremal processes and record events for non-uniformly hyperbolic dynamical systems

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Author(s)

Mark Holland, Mike Todd

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Abstract

For a measure-preserving dynamical system (X, ƒ, μ), we consider the time series of maxima Mn = max{X1,…,Xn} associated to the process Xn = φ (ƒn-1(x)) generated by the dynamical system for some observable φ : Χ → R . Using a point-process approach we establish weak convergence of the process Yn(t) = an(M[nt] - bn) to an extremal Y(t) process for suitable scaling constants an, bn ∈ R . Convergence here takes place in the Skorokhod space D(0, ∞) with the J1 topology. We also establish distributional results for the record times and record values of the corresponding maxima process.
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Original languageEnglish
Pages (from-to)980-1001
JournalErgodic Theory and Dynamical Systems
Volume39
Issue number4
Early online date7 Sep 2017
DOIs
Publication statusPublished - Apr 2019

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