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

• Autorzy: Divanji G.
• Języki publikacji: EN

Abstrakty

EN

Let (X_n, n ≥ 1) be a sequence of independent identically distributed random variables with a common distribution function F and let S_n = ∑ⁿ_{j = 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 (S_n), along with some boundary crossing problems.

Słowa kluczowe

EN

law of iterated logarithm; subsequences; domain of partial attraction; semistable law

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2004
• Tom: Vol. 24, Fasc. 2
• Strony: 433--442
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Divanji G.

• Department of Statistics, Room No 109, Faculty of Science, Addis Ababa University, Post Box No 1176, Addis Ababa, Ethiopia

Bibliografia

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• [6] R. Schwabe and A. Gut, On the law of the iterated logarithm for rapidly increasing subsequences, Math. Nachr. 178 (1996), pp. 309-332.
• [7] E. Seneta, Regularly Varying Functions, Lecture Notes in Math. No 508, Springer, Berlin 1976.
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• [9] J. Slivka and N. C. Savero, On the strong law of large numbers, Proc. Amer. Math. Soc. 24 (1970), pp. 729-734.
• [10] I. Torrång, Law of the iterated logarithm - cluster points of deterministic and random subsequences, Probab. Math. Statist. 8 (1987), pp. 133-141.
• [11] R. Vasudeva, Chover's law of iterated logarithm and weak convergence, Acta Math. Hungar. 44 (3-4) (1984), pp. 215-221.