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Representation of Infinitely Divisible Distributions on Cones

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Abstract

We investigate infinitely divisible distributions on cones in Fréchet spaces. We show that every infinitely divisible distribution concentrated on a normal cone has the regular Lévy–Khintchine representation if and only if the cone is regular. These results are relevant to the study of multidimensional subordination.

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Authors and Affiliations

  1. Centro de Investigación en Matemáticas A. C., Apdo. Postal 402, Guanajuato, Gto., 36000, Mexico

    Victor Pérez-Abreu

  2. Department of Mathematics, University of Tennessee, Knoxville, TN, 39996, USA

    Jan Rosiński

Authors
  1. Victor Pérez-Abreu
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  2. Jan Rosiński
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Correspondence to Victor Pérez-Abreu.

Additional information

Research of J. Rosiński supported by a grant from the National Science Foundation.

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Pérez-Abreu, V., Rosiński, J. Representation of Infinitely Divisible Distributions on Cones. J Theor Probab 20, 535–544 (2007). https://doi.org/10.1007/s10959-007-0076-z

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  • DOI: https://doi.org/10.1007/s10959-007-0076-z

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