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- W2020880153 abstract "{ X n , n ≧ 1} are i.i.d. unbounded random variables with continuous d.f. F ( x ) =1 — e –R ( x ) . X j is a record value of this sequence if X j >max { X 1 , …, X j- 1 } The almost sure behavior of the sequence of record values { X L n } is studied. Sufficient conditions are given for lim sup n→∞ X Ln / R –l ( n )= e c , lim inf n → ∞ X Ln / R −1 ( n ) = e −c , a.s., 0 ≦ c ≦ ∞, and also for lim sup n→∞ ( X Ln —R – 1 ( n ))/ a n =1, lim inf n→∞ ( XL n —R – 1 ( n ))/ a n = − 1, a.s., for suitably chosen constants a n . The a.s. behavior of { X L n } is compared to that of the sequence { M n }, where M n = max { X 1 , …, X n }. The method is to translate results for the case where the X n 's are exponential to the general case by means of an extended theory of regular variation." @default.
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- W2020880153 date "1973-09-01" @default.
- W2020880153 modified "2023-09-23" @default.
- W2020880153 title "Almost sure limit points of record values" @default.
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- W2020880153 doi "https://doi.org/10.1017/s0021900200118418" @default.
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