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A new characterization of Laplace functionals and probability generating functionals
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  • Published: June 1991

A new characterization of Laplace functionals and probability generating functionals

  • Paul Ressel1 &
  • Walter Schmidtchen2 

Probability Theory and Related Fields volume 88, pages 195–213 (1991)Cite this article

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  • 2 Citations

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Summary

The well-known and widely used Laplace resp. probability generating functionals are characterized by properties of positive definiteness and continuity. The methods applied come from Harmonic Analysis on semigroups, and allow also intrinsic characterizations for the transforms of infinitely divisible random measures and point processes.

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Author information

Authors and Affiliations

  1. Mathematische-Geographische Fkultät, Katholische Universität Eichstätt, Ostenstrasse 26-28, W-8078, Eichstätt, Federal Republic of Germany

    Paul Ressel

  2. KPMG Deutsche Treuhand-Gesellschaft, Lessingstrasse 3, W-8000, München 2, Federal Republic of Germany

    Walter Schmidtchen

Authors
  1. Paul Ressel
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  2. Walter Schmidtchen
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Cite this article

Ressel, P., Schmidtchen, W. A new characterization of Laplace functionals and probability generating functionals. Probab. Th. Rel. Fields 88, 195–213 (1991). https://doi.org/10.1007/BF01212559

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  • Received: 14 November 1989

  • Revised: 17 October 1990

  • Issue Date: June 1991

  • DOI: https://doi.org/10.1007/BF01212559

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Keywords

  • Stochastic Process
  • Probability Theory
  • Harmonic Analysis
  • Mathematical Biology
  • Point Process
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