The Annals of Probability

A Note on Stationary Gaussian Sequences

Chandrakant M. Deo

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Abstract

Let $\{\xi_n\}$ be a stationary Gaussian sequence with $E(\xi_0) = 0; E(\xi_0 \xi_n) = r_n$. If $n^\alpha r_n \rightarrow 0$ for some $\alpha > 1$, then Strassen's functional law of iterated logarithm applies to $\{\xi_n\}$.

Article information

Source
Ann. Probab., Volume 2, Number 5 (1974), 954-957.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176996561

Digital Object Identifier
doi:10.1214/aop/1176996561

Mathematical Reviews number (MathSciNet)
MR378014

Zentralblatt MATH identifier
0304.60021

JSTOR
links.jstor.org

Subjects
Primary: 60F15: Strong theorems
Secondary: 60G15: Gaussian processes 60G10: Stationary processes

Keywords
Gaussian sequences Strassen's law of iterated logarithm

Citation

Deo, Chandrakant M. A Note on Stationary Gaussian Sequences. Ann. Probab. 2 (1974), no. 5, 954--957. doi:10.1214/aop/1176996561. https://projecteuclid.org/euclid.aop/1176996561


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