Skip to main content

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
Cancel
×
×
Home
  • Home
Article
  • Cited by 3
  • Cited by
    Crossref Citations
    Crossref logo
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.
    Cheng, Raymond and Harris, Charles B. 2015. Mixed-Norm Spaces and Prediction of SαS Moving Averages. Journal of Time Series Analysis, Vol. 36, Issue. 6, p. 853.
    Cheng, R. and Ross, W. T. 2015. Weak parallelogram laws on banach spaces and applications to prediction. Periodica Mathematica Hungarica, Vol. 71, Issue. 1, p. 45.
    Cheng, Raymond 2015. Prediction of stationary Gaussian random fields with incomplete quarterplane past. Journal of Multivariate Analysis, Vol. 139, Issue. , p. 245.
    ×
  • Access

On the linear prediction of some Lp random fields

  • R. Cheng (a1) and C. Houdré (a2)
Abstract

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.

    •
      • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      On the linear prediction of some Lp random fields
      Available formats
      ×
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      On the linear prediction of some Lp random fields
      Available formats
      ×
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      On the linear prediction of some Lp random fields
      Available formats
      ×
Copyright
COPYRIGHT: © Australian Mathematical Society 1999
References
Hide All
[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.
[2]Cambanis, S. and Soltani, R., ‘Prediction of stable processes: Spectral and moving average representations’, Z. Wahrscheinlichkeitstheorie 66 (1984), 593–612.
[3]Cheng, R., ‘Outer factorization of operator valued weight functions on the torus’, Studia Math. 110 (1994), 19–34.
[4]Chiang, T.-P., ‘On linear extrapolation of discrete of discrete homogeneous stochastic field’, Dokl. Akad. Nauk SSSR 112 (1957), 207–210 (In Russian).
[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).
[6]Chiang, T.-P., ‘The prediction theory of stationary random fields. III. Four-fold Wold decompositions’, J. Multivariate Anal. 37 (1991), 46–65.
[7]Helson, H. and Lowdenslager, D., ‘Prediction theory and Fourier series in several variables I, II’, Acta Math. 99 (1958), 165–202;
‘Prediction theory and Fourier series in several variables I, II’, Acta Math. 106 (1961), 175–213.
[8]Houdré, C., ‘Factorization algorithms and non stationary Wiener filtering’, Stochastics Stochastics Rep. 33 (1990), 49–62.
[9]Houdré, C., ‘Linear Fourier and stochastic analysis’, Probab. Theory Related Fields 87 (1990), 167–188.
[10]Houdré, C., ‘On the linear prediction of multivariate (2, P)-bounded processes’, Ann. Probab. 19 (1991), 843–867.
[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.
[12]Korezlioglu, H. and Loubaton, Ph., ‘Spectral factorization of wide sense stationary processes on Z2’, J. Multivariate Anal. 19 (1986), 24–47.
[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.
[14]Masani, P., Norbert Wiener: Collected works, Vol. III (MIT Press, Cambridge, MA, 1981).
[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.
[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.
[17]Singer, I., Best approximation in normed linear spaces by elements of linear subspaces (Springer, New York, 1970).
[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.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *

CAPTCHA *

Skip to the audio challenge
×
MathJax

Keywords:

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 25 *
Loading metrics...

Abstract views

Total abstract views: 27 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 12th June 2018. This data will be updated every 24 hours.

Cancel
Confirm
×