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.
Publié le : 1973-10-14
Classification:
6069,
6030,
6280,
Moving averages,
detection procedures,
average run length,
Gaussian processes,
first passage times,
upper and lower class boundaries
@article{1176996848,
author = {Lai, Tze Leung},
title = {Gaussian Processes, Moving Averages and Quick Detection Problems},
journal = {Ann. Probab.},
volume = {1},
number = {5},
year = {1973},
pages = { 825-837},
language = {en},
url = {http://dml.mathdoc.fr/item/1176996848}
}
Lai, Tze Leung. Gaussian Processes, Moving Averages and Quick Detection Problems. Ann. Probab., Tome 1 (1973) no. 5, pp. 825-837. http://gdmltest.u-ga.fr/item/1176996848/