TY - JOUR
T1 - Weak convergence to extremal processes and record events for non-uniformly hyperbolic dynamical systems
AU - Holland, Mark
AU - Todd, Mike
N1 - 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.
PY - 2019/4
Y1 - 2019/4
N2 - 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.
AB - 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.
U2 - 10.1017/etds.2017.56
DO - 10.1017/etds.2017.56
M3 - Article
SN - 0143-3857
VL - 39
SP - 980
EP - 1001
JO - Ergodic Theory and Dynamical Systems
JF - Ergodic Theory and Dynamical Systems
IS - 4
ER -