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August, 1979 A New Mixing Condition for Stationary Gaussian Processes
Yashaswini Mittal
Ann. Probab. 7(4): 724-730 (August, 1979). DOI: 10.1214/aop/1176994993

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.

Citation

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Yashaswini Mittal. "A New Mixing Condition for Stationary Gaussian Processes." Ann. Probab. 7 (4) 724 - 730, August, 1979. https://doi.org/10.1214/aop/1176994993

Information

Published: August, 1979
First available in Project Euclid: 19 April 2007

zbMATH: 0412.60046
MathSciNet: MR537217
Digital Object Identifier: 10.1214/aop/1176994993

Subjects:
Primary: 60G10
Secondary: 60G15

Rights: Copyright © 1979 Institute of Mathematical Statistics

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Vol.7 • No. 4 • August, 1979
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