Prediction of level crossings for normal processes containing deterministic components
- 1 March 1979
- journal article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 11 (1) , 93-117
- https://doi.org/10.2307/1426770
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
This publication has 2 references indexed in Scilit:
- Functional limits of empirical distributions in crossing theoryStochastic Processes and their Applications, 1977
- Level Crossings of a Stochastic Process with Absolutely Continuous Sample PathsThe Annals of Probability, 1977