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
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
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