Weak convergence to extremal processes and record events for non-uniformly hyperbolic dynamical systems
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.
Citation
Holland , 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 . https://doi.org/10.1017/etds.2017.56
Publication
Ergodic Theory and Dynamical Systems
Status
Peer reviewed
ISSN
0143-3857Type
Journal article
Rights
© Cambridge University Press, 2017. This work has been made available online in accordance with the publisher’s policies. This is the author created accepted version manuscript following peer review and as such may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1017/etds.2017.56
Description
This 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.Collections
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