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Contents of PMS, Vol. 22, Fasc. 2,
pages 343 - 354
 

THE RATE OF CONVERGENCE IN THE PRECISE LARGE DEVIATION THEOREM

Aleksandras Baltrūnas

Abstract: Let X ,X ,... 1 2 be i.i.d. random variables with a common d.f. F. Let S = X + ...+ X ,n > 1, n 1 n and M = max X ,n > 1. n k<n k In this paper for a large class of subexponential distributions we estimate the rate of convergence

D (t) = P (S > t)- P(M > t), n n n
where n > 1 and t > 0. We close this paper with some examples.

2000 AMS Mathematics Subject Classification: Primary 60F10; Secondary 60E05.

Key words and phrases: Limit theorems, large deviations, subexponential distributions.

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