Conditions for the convergence in distribution of maxima of stationary normal processes |
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Authors: | MR Leadbetter G Lindgren H Rootzén |
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Institution: | Department of Statistics, University of North Carolina, Chapel Hill, NC 27514, USA;Department of Mathematical Statistics, University of Umeå, S-901 87 Umeå, Sweden;Department of Mathematical Statistics, Box 725, S-220 07 LUND, Sweden |
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Abstract: | The asymptotic distribution of the maximum Mn=max1?t?nξt in a stationary normal sequence ξ1,ξ,… depends on the correlation rt between ξ0 and ξt. It is well known that if rt log t → 0 as t → ∞ or if Σr2t<∞, 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. |
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Keywords: | Primary 60G15 60G10 Stationary normal sequences Stationary normal processes Limit distribution for maxima |
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