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Multivariate extremal processes generated by independent non-identically distributed random variables

Published online by Cambridge University Press:  14 July 2016

Ishay Weissman
Ishay Weissman*
Affiliation:
Tel-Aviv University
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Abstract

Let be the kth largest among Xn1, …, Xn[nt], where Xni = (Xi – an)/bn, {Xi} is a sequence of independent random variables and bn > 0 and an are norming constants. Suppose that for each converges in distribution. Then all the finite-dimensional laws of converge. The limiting process is represented in terms of a non-homogeneous two-dimensional Poisson process.

Keywords

MULTIVARIATE K-DIMENSIONAL EXTREMAL PROCESSNON-HOMOGENEOUS TWO-DIMENSIONAL POISSON PROCESSCONVERGENCE OF FINITE-DIMENSIONAL LAWS
Type
Research Papers
Information
Journal of Applied Probability , Volume 12 , Issue 3 , September 1975 , pp. 477 - 487
Copyright
Copyright © Applied Probability Trust 1975 

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References

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