Sankhya: The Indian Journal of Statistics

1999, Volume 61, Series A, Pt. 1 ,pp. 50--61

ALMOST SURE LIMIT SETS OF SEQUENCES OF MAXIMA AND MOVING MAXIMA

By

H.V. HEBBAR and N. VADIRAJA University of Mysore, Manasagangotri

SUMMARY. Suppose {Xn, n>=1} is a sequence of independent random variables (r.v's) with the common distribution function (d.f) F. Define maxima Mn=max(X1, X2,...., Xn), moving maxima
Yk(n)=max(Xn+1, Xn+2,...., Xn+k(n)) where k(n) is a sequence of positive integers. Under certain conditions on F and k(n), the almost sure limit sets of vector sequences comprising properly normalised
Mn and Yk(n) are determined.

AMS (1991) subject classification.Primary 60F15; secondary 60G17.

Key words and phrases. Maxima, moving maxima, almost sure limit set, vector sequence.

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