UNIVERSITY
OF WROCŁAW
 
Main Page
Contents of previous volumes
Forthcoming papers
General Information
Instructions for authors


VOLUMES
39.1 38.2 38.1 37.2 37.1 36.2 36.1
35.2 35.1 34.2 34.1 33.2 33.1 32.2
32.1 31.2 31.1 30.2 30.1 29.2 29.1
28.2 28.1 27.2 27.1 26.2 26.1 25.2
25.1 24.2 24.1 23.2 23.1 22.2 22.1
21.2 21.1 20.2 20.1 19.2 19.1 18.2
18.1 17.2 17.1 16.2 16.1 15 14.2
14.1 13.2 13.1 12.2 12.1 11.2 11.1
10.2 10.1 9.2 9.1 8 7.2 7.1
6.2 6.1 5.2 5.1 4.2 4.1 3.2
3.1 2.2 2.1 1.2 1.1
 
 
WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

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.

Download:    Abstract    Full text   Abstract + References