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Prediction of level crossings for normal processes containing deterministic components

Published online by Cambridge University Press:  01 July 2016

Georg Lindgren
Georg Lindgren*
Affiliation:
University of Umeå
*
∗Postal address: Department of Statistics, University of Umeå, S–90187 Umeå, Sweden.
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Abstract

A level crossing predictor is a predictor process Y(t) which can be used to predict whether a specific process X(t) will cross a predetermined level or not. A natural criterion of 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.

Suppose the process X(t) consists of a deterministic part A(t) which can be calculated with sufficient accuracy, and a stochastic part Xe(t) which can be predicted by some statistically based predictor An example of this is the prediction of water level near a coast, when A(t) is a sum of known tide components.

The paper develops a tool to handle the detection properties of such predictor processes when used to predict level crossings for the case when A(t) is periodic or is a sum of such functions.

Keywords

PREDICTIONLEVEL CROSSINGSGAUSSIAN PROCESSERGODIC THEORY
Type
Research Article
Information
Advances in Applied Probability , Volume 11 , Issue 1 , March 1979 , pp. 93 - 117
Copyright
Copyright © Applied Probability Trust 1979 

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