Open Access
Translator Disclaimer
October 1997 Strong approximation theorems for geometrically weighted random series and their applications
Li-Xin Zhang
Ann. Probab. 25(4): 1621-1635 (October 1997). DOI: 10.1214/aop/1023481105

Abstract

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.

Citation

Download Citation

Li-Xin Zhang. "Strong approximation theorems for geometrically weighted random series and their applications." Ann. Probab. 25 (4) 1621 - 1635, October 1997. https://doi.org/10.1214/aop/1023481105

Information

Published: October 1997
First available in Project Euclid: 7 June 2002

zbMATH: 0903.60017
MathSciNet: MR1487430
Digital Object Identifier: 10.1214/aop/1023481105

Subjects:
Primary: 60F05, 60F15

Rights: Copyright © 1997 Institute of Mathematical Statistics

JOURNAL ARTICLE
15 PAGES


SHARE
Vol.25 • No. 4 • October 1997
Back to Top