## The Annals of Mathematical Statistics

### Asymptotic Properties of Gaussian Processes

#### Abstract

We study separable mean zero Gaussian processes $X(t)$ with correlation $\rho (t, s)$ for which $1 - \rho (t, s)$ is asymptotic to a regularly varying (at zero) function of $|t - s|$ with exponent $0 < \alpha \leqq 2$. For such processes, we obtain the asymptotic distribution of the maximum of $X(t)$. This result is used to obtain a result for $X(t)$ as $t \rightarrow \infty$ similar to the so-called law of the iterated logarithm.

#### Article information

Source
Ann. Math. Statist., Volume 43, Number 2 (1972), 580-596.

Dates
First available in Project Euclid: 27 April 2007

https://projecteuclid.org/euclid.aoms/1177692638

Digital Object Identifier
doi:10.1214/aoms/1177692638

Mathematical Reviews number (MathSciNet)
MR307318

Zentralblatt MATH identifier
0247.60031

JSTOR