Hostname: page-component-7bb8b95d7b-fmk2r Total loading time: 0 Render date: 2024-09-19T10:50:38.801Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

[1] Gihman, I. I. and Skorohod, A. V., The Theory of Stochastic Processes, Springer-Verlag, Berlin, 1974.Google Scholar
[2] Rozanov, Yu. A., Stationary random processes, Holden-Day, San Francisco, 1967.Google Scholar
[3] Hida, T. and Kallianpur, G., The square of a Gaussian Markov process ana nonlinear prediction, Multivar. Anal., 5 No. 4 (1975), 451–461.Google Scholar
[4] Balakrishnan, A. V., Prediction theory for Markoff processes, Pacific J. Math., 11 (1961), 1171–1182.Google Scholar
[5] , A. M. , 1960, , (1962), 275–296.Google Scholar
[6] 2, (1975), 84–95.Google Scholar