Weak convergence to extremal processes and record events for non-uniformly hyperbolic dynamical systems
Holland, MP; Todd, M
Date: 7 September 2017
Article
Journal
Ergodic Theory and Dynamical Systems
Publisher
Cambridge University Press (CUP)
Publisher DOI
Abstract
For a measure-preserving dynamical system (X , f, µ), we consider the time
series of maxima Mn = max{X1, . . . , Xn} associated to the process Xn = φ( f
n−1
(x))
generated by the dynamical system for some observable φ : X → R. Using a pointprocess
approach we establish weak convergence of the process Yn(t) = an(M[nt] − bn)
to an ...
For a measure-preserving dynamical system (X , f, µ), we consider the time
series of maxima Mn = max{X1, . . . , Xn} associated to the process Xn = φ( f
n−1
(x))
generated by the dynamical system for some observable φ : X → R. Using a pointprocess
approach we establish weak convergence of the process Yn(t) = an(M[nt] − bn)
to an extremal process Y (t) 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.
Mathematics and Statistics
Faculty of Environment, Science and Economy
Item views 0
Full item downloads 0