THE RATE OF CONVERGENCE IN THE PRECISE LARGE DEVIATION
THEOREM
Abstract: Let
be i.i.d. random variables with a common d.f.
Let
and
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](files/22.2/HTML/22.2.12.abs5x.png)
where
![n > 1](files/22.2/HTML/22.2.12.abs6x.png)
and
![t > 0.](files/22.2/HTML/22.2.12.abs7x.png)
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.