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The tail process and tail measure of continuous time regularly varying stochastic processes
Ist Teil von
Extremes (Boston), 2022-03, Vol.25 (1), p.107-173
Ort / Verlag
New York: Springer US
Erscheinungsjahr
2022
Link zum Volltext
Quelle
EBSCOhost Business Source Ultimate
Beschreibungen/Notizen
The goal of this paper is to investigate the tools of extreme value theory originally introduced for discrete time stationary stochastic processes (time series), namely the tail process and the tail measure, in the framework of continuous time stochastic processes with paths in the space
D
of càdlàg functions indexed by
ℝ
, endowed with Skorohod’s
J
1
topology. We prove that the essential properties of these objects are preserved, with some minor (though interesting) differences arising. We first obtain structural results which provide representation for homogeneous shift-invariant measures on
D
and then study regular variation of random elements in
D
. We give practical conditions and study several examples, recovering and extending known results.