## The Annals of Probability

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

### A Note on Stationary Gaussian Sequences

#### 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