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Model processes in nonlinear prediction with application to detection and alarm

Lindgren, Georg LU (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)
Please use this url to cite or link to this publication:
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
f7040da0-40c6-422e-ae2a-d3b4c4ad2954 (old id 1273172)
alternative location
http://www.jstor.org/stable/2242825?origin=JSTOR-pdf
date added to LUP
2008-12-09 14:49:57
date last changed
2016-04-16 06:31:02
@misc{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    = {ARRAY(0xa1d7a38)},
  series       = {Annals of Probability},
  title        = {Model processes in nonlinear prediction with application to detection and alarm},
  volume       = {8},
  year         = {1980},
}