### 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)

Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1273172

- author
- Lindgren, Georg
^{LU} - organization
- publishing date
- 1980
- 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
- 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}}, }