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The intrinsic random functions and their applications

  • G. Matheron (a1)
Abstract

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.

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References
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[1] Cramer, H. and Leadbetter, M. R. (1969) Stationary and Related Stochastic Processes. Wiley, New York.
[2] Feller, W. (1957) An Introduction to Probability Theory and its Applications. Vol. 1. Wiley, New York.
[3] Guelfand, M. and Vilenkin, N. Y. (1961) Nekotorye primenenia garmonitsheskovo analisa. Moscow.
[4] Guelfand, M. and Vilenkin, N. Y. (1967) Les Distributions. Vol. 4. Dunod, Paris.
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[6] Guibal, D. (1972) Simulations de schémas intrinsèques. Internal report, Centre de Morphologie Mathématique, Fontainebleau.
[7] Huijbregts, Ch. and Matheron, G. (1970) Universal Kriging — an optimal method for estimating and contouring in trend surface analysis. CIMM International Symposium, Montreal.
[8] Matheron, G. (1969) Le Krigeage Universel. Fasc. No. 1, Cahiers du Centre de Morphologie Mathématique, Fontainebleau.
[9] Matheron, G. (1971) The theory of regionalized variables, and its applications. Fasc. No. 5, Cahiers du Centre de Morphologie Mathématique, Fontainebleau.
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Advances in Applied Probability
  • ISSN: 0001-8678
  • EISSN: 1475-6064
  • URL: /core/journals/advances-in-applied-probability
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