Tid: 20 april 1998 kl 1515-1700
Plats : Seminarierummet 3733, Institutionen för matematik, KTH, Lindstedts väg 25, plan 7. Karta!
Föredragshållare: Elisabeth Pancheva, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences. (Publikationslista)
Titel: Multivariate extremal processes
Extremal processes are random processes with right-continuous increasing sample functions and independent max-increments.
With an extremal process we associate a lower curve , increasing and right-continuous, below which the sample functions of cannot pass. Any extremal process determines uniquely its lower curve.
An extremal process is generated by a Bernoulli point process and has a decomposition as the maximum of two independent point processes with the same lower curve as the original process. The process is the continuous part, and contains the fixed discontinuities of . For a real-valued extremal process the decomposition is unique; for a multivariate extremal process uniqueness breaks down, due to blotting.
Given an extremal process with lower curve and
associated point process , we use a sequence of
max-automorphisms as time-space changes, and study the
limit behaviour of the sequence of extremal processes
under a regularity condition on the norming sequence
and asymptotic negligibility of the max-increments. The
limit class consists of self-similar extremal processes.
The univariate marginals of the limiting extremal process
are max-selfdecomposable. If additionally the initial
extremal process is supposed to have homogeneous
max-increments, then the limiting process is max-stable.
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