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dc.contributor.authorHolland, Mark
dc.contributor.authorTodd, Mike
dc.identifier.citationHolland , M & Todd , M 2019 , ' Weak convergence to extremal processes and record events for non-uniformly hyperbolic dynamical systems ' , Ergodic Theory and Dynamical Systems , vol. 39 , no. 4 , pp. 980-1001 .
dc.identifier.otherORCID: /0000-0002-0042-0713/work/54181504
dc.descriptionThis research was partially supported by the London Mathematics Society (Scheme 4, no. 41126), and both authors thank the Erwin Schroedigner Institute (ESI) in Vienna were part of this work was carried out. MH wishes to thank the Department of Mathematics, University of Houston for hospitality and financial support, and MT thanks Exeter University for their hospitality and support.en
dc.description.abstractFor 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.
dc.relation.ispartofErgodic Theory and Dynamical Systemsen
dc.subjectQA Mathematicsen
dc.titleWeak convergence to extremal processes and record events for non-uniformly hyperbolic dynamical systemsen
dc.typeJournal articleen
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.description.statusPeer revieweden

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