• 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.