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<p>In this paper, we construct a new family of infinitely divisible probability measures, concentrated on a proper cone, with a flexible parametrization. This construction permits to define from any infinitely divisible distribution on the real line, a new multivariate cone-valued probability measure. A characterization of a sub-class of these distributions satisfying a sufficient condition in terms of the Lévy measure, is established. Moreover, several properties, such as the explicit form of the Lévy measure and the closedness under scaling and convolution, are provided. These results extend previous constructions of cone valued gamma and the multivariate stable distributions. The proposed approach is used to build a generalized cone valued inverse-Gaussian distribution, for which, a numerical illustration is performed.</p>

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A Class of Multivariate Cone-Valued Infinitely Divisible Probability Distributions

  • 期刊论文

  • 发表日期：

    2026年2月24日

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  • Afif Masmoudi,
  • Khalil Masmoudi,
  • Hajer Rejeb

摘要

In this paper, we construct a new family of infinitely divisible probability measures, concentrated on a proper cone, with a flexible parametrization. This construction permits to define from any infinitely divisible distribution on the real line, a new multivariate cone-valued probability measure. A characterization of a sub-class of these distributions satisfying a sufficient condition in terms of the Lévy measure, is established. Moreover, several properties, such as the explicit form of the Lévy measure and the closedness under scaling and convolution, are provided. These results extend previous constructions of cone valued gamma and the multivariate stable distributions. The proposed approach is used to build a generalized cone valued inverse-Gaussian distribution, for which, a numerical illustration is performed.