# Lund University Publications

## LUND UNIVERSITY LIBRARIES

### Model processes in nonlinear prediction with application to detection and alarm

(1980) In Annals of Probability 8(4). p.775-792
Abstract
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... (More)
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. (Less)
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Annals of Probability
volume
8
issue
4
pages
775 - 792
publisher
Institute of Mathematical Statistics
ISSN
0091-1798
language
English
LU publication?
yes
id
alternative location
http://www.jstor.org/stable/2242825?origin=JSTOR-pdf
2016-04-04 09:18:23
date last changed
2019-03-08 03:04:18
```@article{f7040da0-40c6-422e-ae2a-d3b4c4ad2954,
abstract     = {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.},
author       = {Lindgren, Georg},
issn         = {0091-1798},
language     = {eng},
number       = {4},
pages        = {775--792},
publisher    = {Institute of Mathematical Statistics},
series       = {Annals of Probability},
title        = {Model processes in nonlinear prediction with application to detection and alarm},
url          = {http://www.jstor.org/stable/2242825?origin=JSTOR-pdf},
volume       = {8},
year         = {1980},
}

```