Self-similar extremal processes |
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Authors: | E I Pancheva |
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Institution: | (1) Institute of Mathematics and Informatics, BAS, 1113 Sofia, Bulgaria |
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Abstract: | Given an extremal process X: 0,∞)→0,∞)d with lower curve C and associated point process N={(tk, Xk):k≥0}, tk distinct and Xk independent, given a sequence ζ
n
=(τ
n
, ξ
n
), n≥1, of time-space changes (max-automorphisms of 0,∞)d+1), we study the limit behavior of the sequence of extremal processes Yn(t)=ξ
n
-1
○ X ○ τn(t)=Cn(t) V max {ξ
n
-1
○ Xk: tk ≤ τn(t){ ⇒ Y under a regularity condition on the norming sequence ζn and asymptotic negligibility of the max-increments of Yn. The limit class consists of self-similar (with respect to a group ηα=(σα, Lα), α>0, of time-space changes) extremal processes. By self-similarity here we mean the property Lα ○ Y(t)
=
d
Y ○ αα(t) for all α>0. The univariate marginals of Y are max-self-decomposable. If additionally the initial extremal process X is
assumed to have homogeneous max-increments, then the limit process is max-stable with homogeneous max-increments.
Supported by the Bulgarian Ministry of Education and Sciences (grant No. MM 234/1996).
Proceedings of the Seminar on Stability Problems for Stochastic Models, Hajdúszoboszló, Hungary, 1997, Part I. |
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Keywords: | |
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