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Variations de champs gaussiens stationnaires: application a l'identification
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  • Published: 01 June 1987

Variations de champs gaussiens stationnaires: application a l'identification

  • Xavier Guyon1 

Probability Theory and Related Fields volume 75, pages 179–193 (1987)Cite this article

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Summary

Let \(X_t ,t \in \mathbb{R}^d \) be a stationary Gaussian random field, with covariance R. For d=1 and d=2, families of variations are described. The convergence in mean square of these variations and a subsequent identification of a model for X are studied. Under suitable glocal conditions for R, the behaviour of these variations depends on the local behaviour of R near the origin. The differences between the case d=1 and d=2 are particularly emphasised: for d=1, there exists only one variation; for d=2, several families of variations are available which provided a useful tool for identifying different models: for example, Orstein-Uhlenbeck processes can be identified in mean square on \(\mathbb{R}\), but not on \(\mathbb{R}\).

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Authors and Affiliations

  1. Université de Paris I, 12 Place du Panthéon, F-75005, Paris, France

    Xavier Guyon

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  1. Xavier Guyon
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Guyon, X. Variations de champs gaussiens stationnaires: application a l'identification. Probab. Th. Rel. Fields 75, 179–193 (1987). https://doi.org/10.1007/BF00354032

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  • Received: 11 June 1983

  • Revised: 07 November 1986

  • Published: 01 June 1987

  • Issue Date: June 1987

  • DOI: https://doi.org/10.1007/BF00354032

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Keywords

  • Covariance
  • Stochastic Process
  • Probability Theory
  • Statistical Theory
  • Random Field
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