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 tex2html_wrap_inline6 we associate a lower curve tex2html_wrap_inline8 , increasing and right-continuous, below which the sample functions of tex2html_wrap_inline6 cannot pass. Any extremal process determines uniquely its lower curve.

An extremal process tex2html_wrap_inline6 is generated by a Bernoulli point process tex2html_wrap_inline24 and has a decomposition tex2html_wrap_inline12 as the maximum of two independent point processes with the same lower curve as the original process. The process tex2html_wrap_inline14 is the continuous part, and tex2html_wrap_inline16 contains the fixed discontinuities of tex2html_wrap_inline6 . 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 tex2html_wrap_inline14 with lower curve tex2html_wrap_inline8 and associated point process tex2html_wrap_inline24 , we use a sequence of max-automorphisms tex2html_wrap_inline26 as time-space changes, and study the limit behaviour of the sequence of extremal processes tex2html_wrap_inline28 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 tex2html_wrap_inline14 is supposed to have homogeneous max-increments, then the limiting process is max-stable.

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