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On Some Local, Global and Regularity Behaviour of Some Classes of Covariance Functions

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Advances and Challenges in Space-time Modelling of Natural Events

Part of the book series: Lecture Notes in Statistics ((LNSP,volume 207))

Abstract

Two critical properties of stationary random fields are their degree of smoothness and the rate of decay of correlation at long lags. These properties are in turn closely connected to the behaviour of the random fields’ spectral densities at infinity and at the origin, respectively. Many standard models have flexibility at one but not both of these scales. Recent works have proposed a number of models with at least some flexibility at both scales. This chapter summarizes some of these proposed models and analyzes their local and global behaviour, both in terms of their covariance functions and the associated spectra. Some ways to obtain models allowing greater flexibility are described.

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Authors and Affiliations

  1. Facultad de Derecho y Ciencias Sociales, Universität Göttingen, Institut for Mathematics Stochastics, Universidad de Castilla-La Mancha, Área de Estadística, Avenida Camilo Jose Cela 14, 13005, Ciudad Real, España

    Emilio Porcu

  2. Department of Statistics, The University of Chicago, Chicago, USA

    Michael L. Stein

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  1. Emilio Porcu
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  2. Michael L. Stein
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Correspondence to Emilio Porcu .

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Editors and Affiliations

  1. Facultad de Derecho y Ciencias Sociales, Área de Estadística, Universidad de Castilla la Mancha, Avenida Camilo Jose Cela 14, Ciudad Real, 13005, Spain

    Emilio Porcu

  2. , Statistics, Universidad de Castilla la Mancha, Cobertizo San Pedro Martir, Toledo, 45071, Spain

    José–María Montero

  3. , Mathematics Stochastics, Universität Göttingen, Goldschmidtstrasse 7, Göttingen, 37077, Germany

    Martin Schlather

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Porcu, E., Stein, M.L. (2012). On Some Local, Global and Regularity Behaviour of Some Classes of Covariance Functions. In: Porcu, E., Montero, J., Schlather, M. (eds) Advances and Challenges in Space-time Modelling of Natural Events. Lecture Notes in Statistics(), vol 207. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17086-7_9

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