Hostname: page-component-7bb8b95d7b-s9k8s Total loading time: 0 Render date: 2024-10-02T15:56:01.995Z Has data issue: false hasContentIssue false
  • English
  • Français

On the linear prediction of some Lp random fields

Part of: Stochastic processes

Published online by Cambridge University Press:  09 April 2009

R. Cheng  and
C. Houdré
R. Cheng
Affiliation:
Executive Vice President ECI Systems and Engineering 596 Lynnhaven Parkway Virginia Beach, VA 23452USA e-mail: [email protected]
C. Houdré
Affiliation:
South East Applied Analysis Center School of Mathematics Georgia Institute of TechnologyAtlanta, GA 30332 USA e-mail: [email protected]
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.

This work is concerned with the prediction problem for a class of Lp-random fields. For this class of fields, we derive prediction error formulas, spectral factorizations, and orthogonal decompositions.

Keywords

Predictionrandom fields.

MSC classification

Secondary: 60G25: Prediction theory 60G60: Random fields 60G10: Stationary processes
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 67 , Issue 1 , August 1999 , pp. 31 - 50
Copyright
Copyright © Australian Mathematical Society 1999

References

[1]Cambanis, S., Hardin, C. D. Jr and Weron, A., ‘Innovations and Wold decompositions of stable sequences’, Probab. Theory Related Fields 79 (1988), 1–27.CrossRefGoogle Scholar
[2]Cambanis, S. and Soltani, R., ‘Prediction of stable processes: Spectral and moving average representations’, Z. Wahrscheinlichkeitstheorie 66 (1984), 593–612.CrossRefGoogle Scholar
[3]Cheng, R., ‘Outer factorization of operator valued weight functions on the torus’, Studia Math. 110 (1994), 19–34.Google Scholar
[4]Chiang, T.-P., ‘On linear extrapolation of discrete of discrete homogeneous stochastic field’, Dokl. Akad. Nauk SSSR 112 (1957), 207–210 (In Russian).Google Scholar
[5]Chiang, T.-P., ‘The prediction theory of stationary random fields. I. Half-plane prediction’, Acta Sci. Natur. Univ. Pekinensis 25 (1991), 25–50 (In Chinese with English abstract).Google Scholar
[6]Chiang, T.-P., ‘The prediction theory of stationary random fields. III. Four-fold Wold decompositions’, J. Multivariate Anal. 37 (1991), 46–65.CrossRefGoogle Scholar
[7]Helson, H. and Lowdenslager, D., ‘Prediction theory and Fourier series in several variables I, II’, Acta Math. 99 (1958), 165–202;Google Scholar
‘Prediction theory and Fourier series in several variables I, II’, Acta Math. 106 (1961), 175–213.CrossRefGoogle Scholar
[8]Houdré, C., ‘Factorization algorithms and non stationary Wiener filtering’, Stochastics Stochastics Rep. 33 (1990), 49–62.Google Scholar
[9]Houdré, C., ‘Linear Fourier and stochastic analysis’, Probab. Theory Related Fields 87 (1990), 167–188.CrossRefGoogle Scholar
[10]Houdré, C., ‘On the linear prediction of multivariate (2, P)-bounded processes’, Ann. Probab. 19 (1991), 843–867.CrossRefGoogle Scholar
[11]Korezlioglu, H. and Loubaton, Ph., ‘Prediction and spectral decomposition of wide-sense stationary processes on Z2’, in: Spatial processes and spatial time series analysis (Brussels 1985) (ed. F., Droesbeke) (Publ. Fac. Univ. Saint-Louis, Brussels, 1987), pp. 127–164.Google Scholar
[12]Korezlioglu, H. and Loubaton, Ph., ‘Spectral factorization of wide sense stationary processes on Z2’, J. Multivariate Anal. 19 (1986), 24–47.Google Scholar
[13]Ph., Loubaton, ‘A regularity criterion for lexicographical prediction of multivariate wide-sense stationary processes on Z2 with non-full-rank spectral densities’, J. Funct. Anal. 104 (1992), 198–228.Google Scholar
[14]Masani, P., Norbert Wiener: Collected works, Vol. III (MIT Press, Cambridge, MA, 1981).Google Scholar
[15]Miamee, A. G. and Pourahmadi, M., ‘Wold decomposition, prediction and parameterization of stationary processes with infinite variance’, Probab. Theory Related Fields 79 (1988), 145–164.Google Scholar
[16]Rajput, B. S. and Sundberg, C., ‘On some extremal problems in H p and the prediction of L p-harmonizable stochastic processes’, Probab. Theory Related Fields 99 (1994), 197–210.CrossRefGoogle Scholar
[17]Singer, I., Best approximation in normed linear spaces by elements of linear subspaces (Springer, New York, 1970).CrossRefGoogle Scholar
[18]Spencer, N. M. and Anh, V. V., ‘Spectral factorisation and prediction of multivariate processes with time-dependent spectral density matrices’, J. Austral. Math. Soc. (Ser. B) 33 (1991), 192–210.CrossRefGoogle Scholar