Hostname: page-component-745bb68f8f-kw2vx Total loading time: 0 Render date: 2025-01-28T23:30:48.086Z Has data issue: false hasContentIssue false
  • English
  • Français

Non-linear predictors of transformed stationary processes

Published online by Cambridge University Press:  22 January 2016

Izumi Kubo  and
Sheu-San Lee
Izumi Kubo
Affiliation:
Faculty of Integrated Arts and Sciences, Hiroshima University, Hiroshima, 730, Japan
Sheu-San Lee
Affiliation:
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.

One of the authors discussed the best non-linear predictor of the process X(t) = f(U(t)), which is obtained by transforming an Ornstein-Uhlenbeck process U(t) with a measurable function f(u) (see [5]).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 95 , September 1984 , pp. 23 - 40
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1984

References

[ 1 ] Friedman, A., Stocastic differential equations and applications, Vol. 2, Academic Press, 1976.Google Scholar
[ 2 ] Hida, T., Canonical representation of Gaussian processes and their applications, Mem. Coll. Sci. Univ. Kyoto, 33 (1960), 109–155.Google Scholar
[ 3 ] Ikeda, N. and Watanabe, S., Stochastic differential equations and diffusion processes, North-Holland/Kodansha, 1981.Google Scholar
[ 4 ] Kōno, N., On the modulus of continuity of sample functions of Gaussian processes, J. Math. Kyoto Univ., 10-3 (1970), 493–536.Google Scholar
[ 5 ] Lee, Sheu-San, Non-linear prediction problems for Ornstein-Uhlenbeck process, Nagoya Math. J., 91 (1983), 173–183.CrossRefGoogle Scholar
[ 6 ] McKean, H. P., Stochastic integrals, Academic Press, 1969.Google Scholar
[ 7 ] McKean, H. P., Elementary solutions for certain parabolic partial differential equations, Trans. Amer. Math. Soc, 82 (1956), 519–548.CrossRefGoogle Scholar