Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-29T01:32:17.435Z Has data issue: false hasContentIssue false
  • English
  • Français

On the prediction error for two-parameter stationary random fields

Published online by Cambridge University Press:  17 April 2009

R. Cheng
R. Cheng
Affiliation:
Department of Mathematics, University of Louisville, Louisville KY 40292, United States of America
Rights & Permissions [Opens in a new window]

Abstract

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.

A number of Szegö-type prediction error formulas are given for two-parameter stationary random fields. These give rise to an array of elementary inequalities and illustrate a general duality relation.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 46 , Issue 1 , August 1992 , pp. 167 - 175
Copyright
Copyright © Australian Mathematical Society 1992

References

[1]Cheng, R., ‘A natural decomposition of L 2 spaces on the torus’, (preprint 1990).Google Scholar
[2]Cheng, R., ‘A strong mixing condition for second-order stationary random fields’, (preprint 1990), Studia Math, (to appear).Google Scholar
[3]Helson, H. and Lowdenslager, D., ‘Prediction theory and Fourier series in several variables’, Acta Math. 99 (1959), 165–202.CrossRefGoogle Scholar
[4]Helson, H. and Lowdenslager, D., ‘Prediction theory and Fourier series in several variables II’, Acta Math. 106 (1962), 175–213.Google Scholar
[5]Kallianpur, G., Miamee, A.G. and Niemi, H., On the prediction theory of two-parameter stationary random fields: Center for Stochastic Processes, Technical Report No. 178 (UNC, Chapel Hill, 1987).Google Scholar
[6]Kolmogorov, A.N., ‘Interpolation and Extrapolation von stationären zufälligen Folgen’, Izv. Akad. Nauk SSSR 5 (1941), 3–14.Google Scholar
[7]Miamee, A.G. and Pourahmadi, M., ‘Best approximations in Lp(dμ), and prediction problems of Szegö, Kolmogorov, Yaglom and Nakazi’, J. London Math. Soc. 38 (1988), 133–145.CrossRefGoogle Scholar
[8]Szegö, G., ‘Beiträge zur Theorie der Toeplitzchen Formen’, Math. Z. 6 (1920), 167–202.CrossRefGoogle Scholar