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Non-Linear prediction problems for Ornstein-Uhlenbeck process

Published online by Cambridge University Press:  22 January 2016

Sheu-San Lee
Sheu-San Lee*
Affiliation:
Department of Mathematics, Faculty of Science, Nagoya University, Japan
*
Shenyang Chemical Engineering Institute, Shenyang, China
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We shall discuss in this paper some problems in non-linear prediction theory. An Ornstein-Uhlenbeck process {U(t)} is taken to be a basic process, and we shall deal with stochastic processes X(t) that are transformed by functions f satisfying certain condition. Actually, observed processes are expressed in the form X(t) = f(U(t)). Our main problem is to obtain the best non-linear predictor X̂(t, τ) for X(t + τ), τ > 0, assuming that X(s), s ≤t, are observed. The predictor is therefore a non-linear functional of the values X(s), s ≤ t.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 91 , September 1983 , pp. 173 - 184
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1983

References

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