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

2016/08/19 by Holland, Mark, Todd, Mike
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1608.05620

Abstract

For a measure preserving dynamical system (X,f, μ), we consider the time series of maxima M_n=max\X₁,…,X_n\ associated to the process X_n=ϕ(f^n-1(x)) generated by the dynamical system for some observable ϕ:X→ℝ. Using a point process approach we establish weak convergence of the process Y_n(t)=a_n(M_[nt]-b_n) to an extremal process Y(t) for suitable scaling constants a_n,b_n∈ℝ. Convergence here taking place in the Skorokhod space \mathbbD(0,∞) with the J₁ topology. We also establish distributional results for the record times and record values of the corresponding maxima process.

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