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Law of the iterated logarithm for subsequences of partial sums which are in the domain of partial attraction of a semistable law

Divanji G.

Probability and Mathematical Statistics

2004

Vol. 24, Fasc. 2

433--442

Let (Xn, n ≥ 1) be a sequence of independent identically distributed random variables with a common distribution function F and let Sn = ∑nj = 1, n ≥ 1. When F belongs to the domain of partial attraction of a semistable law with index α, 0 < α < 2, Chover’s form of the law of the iterated logarithm has been obtained for subsequences of (Sn), along with some boundary crossing problems.