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Interpolation, correlation identities, and inequalities for infinitely divisible variables

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Abstract

We present an interpolation formula for the expectation of functions of infinitely divisible (i.d.) variables. This is then applied to study the association problem for i.d. vectors and to present new covariance expansions and correlation inequalities.

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Authors and Affiliations

  1. Southeast Applied Analysis Center, School of Mathematics, Georgia Institute of Technology, 30332, Atlanta, Georgia

    Christian Houdré

  2. Department of Probability and Statistics, Centro de Investigación en Matemáticas, A.C. Apdo. Postal 402, 36000, Guanajuato, Gto, Mexico

    Victor Pérez-Abreu

  3. Institute of Mathematics and Informatics, Lithuanian Academy of Sciences, 2600, Vilnius, Lithuania

    Donatas Surgailis

Authors
  1. Christian Houdré
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  2. Victor Pérez-Abreu
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  3. Donatas Surgailis
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Additional information

Communicated by Abram Kagan

Acknowledgements and Notes. The research of C. Houdré was supported in part by an NSF Mathematical Sciences Post-Doctoral Fellowship and by an NSF-NATO Postdoctoral Fellowship and by the NSF grant No. DMS-98032039. This research was completed while V. Pérez-Abreu was visiting the Georgia Institute of Technology.

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Houdré, C., Pérez-Abreu, V. & Surgailis, D. Interpolation, correlation identities, and inequalities for infinitely divisible variables. The Journal of Fourier Analysis and Applications 4, 651–668 (1998). https://doi.org/10.1007/BF02479672

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  • DOI: https://doi.org/10.1007/BF02479672

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