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Medientyp:
E-Artikel
Titel:
Scheduled Maxima Sequences
Beteiligte:
Deken, Joseph G.
Erschienen:
Applied Probability Trust, 1978
Erschienen in:
Journal of Applied Probability, 15 (1978) 3, Seite 543-551
Sprache:
Englisch
ISSN:
0021-9002
Entstehung:
Anmerkungen:
Beschreibung:
We define a vector-valued scheduled maxima sequence M by considering simultaneously the maxima of several i.i.d. sequences, with the number of observations considered from each sequence at any time determined by a random scheduling sequence J. It is shown that the max-min (vector) sequence\{\vee_{k=1}^{i} Y_k,-\wedge_{k=1}^{i} Y_k\}_{i=1}^\inftyderived from i.i.d. { Yi}i=1 ∞can be represented as a mixture of scheduled maxima sequences, giving results for this sequence and the range$(\vee_{k=1}^{i}Y_k,-\wedge_{k=1}^{i}{Y}_k)$. A functional limit theorem for the scheduled maxima sequence shows convergence to independent extremal processes. Embedding in a scheduled extremal process gives strong laws, central limit theorems, and laws of the iterated logarithm for the record time of the scheduled maxima sequence, and hence for the max-min sequence and the range.