Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-23T07:19:17.923Z Has data issue: false hasContentIssue false
  • English
  • Français

The intrinsic random functions and their applications

Published online by Cambridge University Press:  01 July 2016

G. Matheron
G. Matheron*
Affiliation:
Centre de Morphologie Mathématique, Fontainebleau
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.

The intrinsic random functions (IRF) are a particular case of the Guelfand generalized processes with stationary increments. They constitute a much wider class than the stationary RF, and are used in practical applications for representing non-stationary phenomena. The most important topics are: existence of a generalized covariance (GC) for which statistical inference is possible from a unique realization; theory of the best linear intrinsic estimator (BLIE) used for contouring and estimating problems; the turning bands method for simulating IRF; and the models with polynomial GC, for which statistical inference may be performed by automatic procedures.

Keywords

GUELFAND GENERALIZED STOCHASTIC PROCESSINTRINSIC RANDOM FUNCTIONGENERALIZED COVARIANCESPOLYNOMIAL COVARIANCETURNING BANDS METHOD
Type
Research Article
Information
Advances in Applied Probability , Volume 5 , Issue 3 , December 1973 , pp. 439 - 468
Copyright
Copyright © Applied Probability Trust 1973 

References

[1] Cramer, H. and Leadbetter, M. R. (1969) Stationary and Related Stochastic Processes. Wiley, New York.Google Scholar
[2] Feller, W. (1957) An Introduction to Probability Theory and its Applications. Vol. 1. Wiley, New York.Google Scholar
[3] Guelfand, M. and Vilenkin, N. Y. (1961) Nekotorye primenenia garmonitsheskovo analisa. Moscow.Google Scholar
[4] Guelfand, M. and Vilenkin, N. Y. (1967) Les Distributions. Vol. 4. Dunod, Paris.Google Scholar
[5] Grenander, U. and Rosenblatt, M. (1957) Stationary Time Series. Wiley, New York.Google Scholar
[6] Guibal, D. (1972) Simulations de schémas intrinsèques. Internal report, Centre de Morphologie Mathématique, Fontainebleau.Google Scholar
[7] Huijbregts, Ch. and Matheron, G. (1970) Universal Kriging — an optimal method for estimating and contouring in trend surface analysis. CIMM International Symposium, Montreal.Google Scholar
[8] Matheron, G. (1969) Le Krigeage Universel. Fasc. No. 1, Cahiers du Centre de Morphologie Mathématique, Fontainebleau.Google Scholar
[9] Matheron, G. (1971) The theory of regionalized variables, and its applications. Fasc. No. 5, Cahiers du Centre de Morphologie Mathématique, Fontainebleau.Google Scholar
[10] Orfeuil, J. P. (1972) Simulation du Wiener-Lévy et de ses intégrales. Internal report, Centre de Morphologie Mathématique, Fontainebleau.Google Scholar
[11] Yaglom, A. M. (1962) Stationary Random Functions. Prentice Hall, Englewood Cliffs, N. J. Google Scholar
[12] Wiener, N. and Masani, P. (1958) The prediction theory for multivariate stochastic processes. I. Acta Math. 98, 111–150; II. Acta Math. 99, 93–137.CrossRefGoogle Scholar