The strong approximation of extremal processes |
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Authors: | Paul Deheuvels |
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Institution: | (1) 7, avenue du Château, F-92340 Bourg-la-Reine |
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Abstract: | Summary If X
1, X
2, ..., are i.i.d. random variables and Y
n
=Max(X
1, ..., X
n
); if for some sequences A
n
, Bn, n=1, 2, ..., E
n
(t)=AnYnt]+Bn is such that E
n
(1) weakly converges to a non degenerate limit distribution, then we prove that it is possible to construct a sequence of replicates of extremal processes E
(n)(t) on the same probability space, such that d(E
n
(.), E
(n)(.)) 0 a.s., with the Levy metric. We give the rates of consistency of the approximations. |
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Keywords: | |
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