Lithuanian Mathematical Journal

, Volume 57, Issue 1, pp 59–68 | Cite as

Characterization of multivariate stable processes

  • Mahdi Louati
  • Afif Masmoudi
  • Farouk Mselmi


This paper deals with a characterization of a multivariate stable process using an independence property with a positive random variable. Moreover, we establish a characterization of a multivariate Lévy process based on the notion of cut in a natural exponential family. This allows us to draw some related properties. More precisely, we give the probability density function of this process and the law of the mixture of the Lévy process governed by the convolution semigroup with respect to an exponential random variable. These results are confidentially connected with the univariate case given by [G. Letac and V. Seshadri, Exponential stopping and drifted stable processes, Stat. Probab. Lett., 72:137–143, 2005].


cumulant function infinitely divisible processes Laplace distribution Lévy processes stable distribution 


60G52 44A10 


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© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Sfax National School of Electronics and TelecommunicationSfaxTunisia
  2. 2.Laboratory of Probability and Statistics, Sfax Faculty of SciencesSfaxTunisia

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