On the number of boundary crossings related to LIL and SLLN for record values and partial maxima of i.i.d. sequences and extremes of uniform spacings. (English) Zbl 0770.60033
The moments of the random variables (r.v.) associated with the number of boundary crossings have been considered with respect to (1) the laws of the iterated logarithm for record values and extremes of uniform spacings and (2) the SLLN for partial maxima of i.i.d. r.v.s. The convergence/non- convergence of the moments of these r.v.s have been examined. Further, by applying a result due to C. M. Deo [J. Appl. Probab. 10, 402-408 (1973; Zbl 0273.60018)], the set of all a.s. limit points have been obtained for the normalized sequence of record values considered in (1).
Reviewer: R.Vasudeva (Mysore)
Keywords:
boundary crossings; laws of the iterated logarithm; partial maxima; sequence of record valuesCitations:
Zbl 0273.60018References:
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