A Law of Iterated Logarithm for Delayed Random Sums

Authors

  • Gooty Divanji Department of Studies in Statistics, Manasagangotri, University of Mysore, Mysuru, Karnataka, India

Keywords:

Delayed sums, Delayed random sums, Law of iterated logarithm, Domain of attraction, Stable Law

Abstract

Let Xn , n 1be a sequence of independent identically distributed random variables with
a common distribution function F and let
n
n j
j = 1
S =X , n  1. When F belongs to the domain
of attraction of a stable law with index , 0 <  < 2, Chover's form of the law of the iterated
logarithm has been obtained for delayed random sums.

References

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Chover J. A LIL for stable summands, Proc. Amer. Math. Soc., 1966; 17: 441–443p.

Gooty Divanji. Law of iterated logarithm for subsequences of partial sums which are in the

domain of partial attraction of semi stable law, Probab Math Stat. 2004; 24: Fasc. 2, 41, 433–

p.

Vasudeva R, Divanji G. LIL for delayed sums under a non-identically distributed setup, TPRBAU.

; 37(3): 534–542p.

Spitzer F. Principles of Random Walk. Van Nostrand: Princeton, New Jercey, 1964.

Nielsen OB. On the rate of growth of the partial maxima of a sequence of independent identically

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: 470–472p.

Heyde CC. On large deviation problems for sums of random variables which are not attracted to

the normal law, Ann Math Statist. 1967; 38(5): 1575–1578p.

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Published

2022-03-30

Issue

Vol. 6 No. 1 (2017)

Section

Review Article

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