Conditions for the convergence in distribution of maxima of stationary normal processes
The asymptotic distribution of the maximum Mn=max1[less-than-or-equals, slant]t[less-than-or-equals, slant]n[xi]t in a stationary normal sequence [xi]1,[xi],... depends on the correlation rt between [xi]0 and [xi]t. It is well known that if rt log t --> 0 as t --> [infinity] or if [Sigma]r2t<[infinity], then the limiting distribution is the same as for a sequence of independent normal variables. Here it is shown that this also follows from a weaker condition, which only puts a restriction on the number of t-values for which rt log t islarge. The condition gives some insight into what is essential for this asymptotic behaviour of maxima. Similar results are obtained for a stationary normal process in continuous time.
Year of publication: |
1978
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Authors: | Leadbetter, M. R. ; Lindgren, G. ; Rootzén, H. |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 8.1978, 2, p. 131-139
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Publisher: |
Elsevier |
Saved in:
Online Resource
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