The Annals of Probability

A New Mixing Condition for Stationary Gaussian Processes

Yashaswini Mittal

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Abstract

A new mixing condition is proposed for the study of stationary Gaussian processes on $R^1$. If the covariance function of the process is $r$, assume $$\text{Lebesgue measure}\big\{t\mid 0 \leqslant t \leqslant T; r(t) > \frac{f(t)}{\ln t}\big\} = o(T^\beta)$$ as $T \rightarrow \infty$, for some $0 \leqslant \beta < 1$ and some $f(t) = o(1)$. The stated condition is weaker than those in common use, and yet it is shown to imply the same limit theorems on the distribution of the maximum of the process. Examples are given of processes which satisfy the new condition and not the previous ones.

Article information

Source
Ann. Probab., Volume 7, Number 4 (1979), 724-730.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176994993

Digital Object Identifier
doi:10.1214/aop/1176994993

Mathematical Reviews number (MathSciNet)
MR537217

Zentralblatt MATH identifier
0412.60046

JSTOR
links.jstor.org

Subjects
Primary: 60G10: Stationary processes
Secondary: 60G15: Gaussian processes

Keywords
Stationary Gaussian processes maxima limiting behavior covariance functions

Citation

Mittal, Yashaswini. A New Mixing Condition for Stationary Gaussian Processes. Ann. Probab. 7 (1979), no. 4, 724--730. doi:10.1214/aop/1176994993. https://projecteuclid.org/euclid.aop/1176994993


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