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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.

On Hartman's law of iterated logarithm for explosive Gaussian autoregressive processes

Bercu B., Touati A.

Probability and Mathematical Statistics

2002

Vol. 22, Fasc. 1

101--113

A law of iterated logarithm is established for the maximum likelihood estimator of the unknown parameter of the explosive Gaussian autoregressive process. Outside the Gaussian case, we show that the law of iterated logarithm does not hold, except for a suitable averaging on the maximum likelihood estimator.