Let ${X_n;n\geq 0}$ be a sequence of random variables. We consider
its geometrically weighted series $\xi(\beta)=\sum_{n=0}^\infty \betaX_n$ for
$0<\beta < 1$. This paper proves that $\xi (\beta)$ can be approximated
by $\sum_{n=0}^\infty \beta^n Y_n$ under some suitable conditions, where ${Y_n;
n \geq 0}$ is a sequence of independent normal random variables. Applications
to the law of the iterated logarithm for $\xi(\beta)$ are also discussed.
Publié le : 1997-10-14
Classification:
Geometrically weighted series,
strong approximation,
the law of the iterated logarithm,
60F05,
60F15
@article{1023481105,
author = {Zhang, Li-Xin},
title = {Strong approximation theorems for geometrically weighted random
series and their applications},
journal = {Ann. Probab.},
volume = {25},
number = {4},
year = {1997},
pages = { 1621-1635},
language = {en},
url = {http://dml.mathdoc.fr/item/1023481105}
}
Zhang, Li-Xin. Strong approximation theorems for geometrically weighted random
series and their applications. Ann. Probab., Tome 25 (1997) no. 4, pp. 1621-1635. http://gdmltest.u-ga.fr/item/1023481105/