Let $S_n$ denote the partial sums of i.i.d. random variables with mean zero and moment generating function existing in some neighborhood of the origin. We give explicit upper bounds for $P_m^+ = P(S_n \geqq a + bn$ for some $n \geqq m)$ and $P_m = P(|S_n| \geqq a + bn$ for some $n \geqq m), a \geqq 0, b > 0$. These bounds immediately give the rate of convergence for the strong law of large numbers. An application is also made to a sequential selection procedure.
Publié le : 1973-06-14
Classification:
Upper bound,
rate of convergence,
strong law of large numbers,
moment generating function,
sequential selection procedure,
60G50,
60F99
@article{1176996945,
author = {Khan, Rasul A.},
title = {A Note on the Rate of Convergence and Its Applications},
journal = {Ann. Probab.},
volume = {1},
number = {5},
year = {1973},
pages = { 504-508},
language = {en},
url = {http://dml.mathdoc.fr/item/1176996945}
}
Khan, Rasul A. A Note on the Rate of Convergence and Its Applications. Ann. Probab., Tome 1 (1973) no. 5, pp. 504-508. http://gdmltest.u-ga.fr/item/1176996945/