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October, 1973 Gaussian Processes, Moving Averages and Quick Detection Problems
Tze Leung Lai
Ann. Probab. 1(5): 825-837 (October, 1973). DOI: 10.1214/aop/1176996848

Abstract

In this paper, we are interested in moving averages of the type $\int^t_0 f(t - s) dX(s)$, where $X(t)$ is a Wiener process and $\int^\infty_0 f^2(t) dt < \infty$. By a suitable choice of the weighting function $f$, such processes can be used to detect a change in the drift of $X(t)$. First passage times of these moving-average processes and more general Gaussian processes are studied. Limit theorems for Gaussian processes and Gaussian sequences which include these moving-average processes and their discrete-time analogs as special cases are also proved.

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Tze Leung Lai. "Gaussian Processes, Moving Averages and Quick Detection Problems." Ann. Probab. 1 (5) 825 - 837, October, 1973. https://doi.org/10.1214/aop/1176996848

Information

Published: October, 1973
First available in Project Euclid: 19 April 2007

zbMATH: 0294.60028
MathSciNet: MR365679
Digital Object Identifier: 10.1214/aop/1176996848

Keywords: 6030 , 6069 , 6280 , average run length , detection procedures , first passage times , Gaussian processes , moving averages , upper and lower class boundaries

Rights: Copyright © 1973 Institute of Mathematical Statistics

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Vol.1 • No. 5 • October, 1973
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