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

Ergodic Theory and Dynamical Systems


For a measure-preserving dynamical system (X, ƒ, μ), we consider the time series of maxima M<sub>n</sub> = max{X<sub>1</sub>,…,X<sub>n</sub>} associated to the process Xn = φ (ƒ<sup>n-1</sup>(x)) generated by the dynamical system for some observable φ : Χ → R . Using a point-process approach we establish weak convergence of the process Y<sub>n</sub>(t) = a<sub>n</sub>(M<sub>[nt]</sub> - b<sub>n</sub>) to an extremal Y(t) process for suitable scaling constants a<sub>n</sub>, b<sub>n</sub> ∈ R . Convergence here takes place in the Skorokhod space D(0, ∞) with the J<sub>1</sub> topology. We also establish distributional results for the record times and record values of the corresponding maxima process.

Mark Holland


Year of publication: 2019

Volume: 39

Issue: 4

Pages: 980--1001


Other: 2-s2.0-85062224313


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