Joseph Mecke’s Last Fragmentary Manuscripts - a Compilation

  • W. NagelEmail author
  • V. Weiß
Probability Theory and Mathematical Statistics


Summarizing results from Joseph Mecke’s last fragmentary manuscripts, the generating function and the Laplace transform for nonnegative random variables are considered. The concept of thickening of a random variable, as an inverse operation to thinning (which is usually applied to point processes) is introduced, based on generating functions, and a characterization of thickable random variables is given. Further, some new relations between exponential distributions and their interpretation in terms of Poisson point processes are derived with the help of the Laplace transform.


Generating function Laplace transform thinning of a point process exponential distribution 

MSC2010 numbers

60E10 60G55 


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  1. 1.
    R. V. Ambartzumian, “On condensable point processes”, In: V.V. Sazonov, T.L. Shervashidze, (eds.): New Trends in Probability and Statististics, VSP, Mokslas, Utrecht, Vilnius, 655–667, 1991.Google Scholar
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    J. Mecke, Random Measures (WalterWarmuth Verlag, Berlin, 2011).zbMATHGoogle Scholar
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Copyright information

© Allerton Press, Inc. 2019

Authors and Affiliations

  1. 1.Friedrich-Schiller-UniversitätJenaGermany
  2. 2.Ernst-Abbe-HochschuleJenaGermany

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