| Title | Model processes in nonlinear prediction with application to detection and alarm |
| Authors | Georg Lindgren |
| Alternative Location | http://www.jstor.org/stable..., Restricted Access |
| Publication | Annals of Probability |
| Year | 1980 |
| Volume | 8 |
| Issue | 4 |
| Pages | 775 - 792 |
| Document type | Article |
| Status | Published |
| Quality controlled | Yes |
| Language | eng |
| Abstract English | A level crossing predictor is a predictor process $Y(t)$, possibly multivariate, which can be used to predict whether a specified process $X(t)$ will cross a predetermined level or not. A natural criterion on how good a predictor is, can be the probability that a crossing is detected a sufficient time ahead, and the number of times the predictor makes a false alarm. If $X$ is Gaussian and the process $Y$ is designed to detect only level crossings, one is led to consider a multivariate predictor process $Y(t)$ such that a level crossing is predicted for $X(t)$ if $Y(t)$ enters some nonlinear region in $R^p$. In the present paper we develop the probabilistic methods for evaluation of such an alarm system. The basic tool is a model for the behavior of $X(t)$ near the points where $Y(t)$ enters the alarm region. This model includes the joint distribution of location and direction of $Y(t)$ at the crossing points. |
| ISBN/ISSN/Other | ISSN: 0091-1798 |
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