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The Lévy-Itô decomposition in free probability
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  • Published: 09 October 2004

The Lévy-Itô decomposition in free probability

  • O.E. Barndorff-Nielsen1 &
  • S. Thorbjørnsen2 

Probability Theory and Related Fields volume 131, pages 197–228 (2005)Cite this article

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Abstract.

In this paper we prove the free analog of the Lévy-Itô decomposition for Lévy processes. A significant part of the proof consists of introducing free Poisson random measures, proving their existence and developing a theory of integration with respect to such measures. The existence of free Poisson random measures also yields, via the free Lévy-Itô decomposition, an alternative proof of the general existence of free Lévy processes (in law).

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Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, University of Aarhus, Ny Munkegade, 8000, Aarhus C, Denmark

    O.E. Barndorff-Nielsen

  2. Department of Mathematics and Computer Science, University of Southern Denmark, Campusvej 55, 5230, Odense M, Denmark

    S. Thorbjørnsen

Authors
  1. O.E. Barndorff-Nielsen
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  2. S. Thorbjørnsen
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Corresponding author

Correspondence to O.E. Barndorff-Nielsen.

Additional information

MaPhySto – The Danish National Research Foundation Network in Mathematical Physics and Stochastics

Supported by the Danish Natural Science Research Council

Mathematics Subject Classification (2000): Primary 46L54; Secondary 60G20, 60G57

Acknowledgement We are grateful to the referee for many helpful remarks.

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Barndorff-Nielsen, O., Thorbjørnsen, S. The Lévy-Itô decomposition in free probability. Probab. Theory Relat. Fields 131, 197–228 (2005). https://doi.org/10.1007/s00440-003-0322-y

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  • Received: 10 April 2003

  • Revised: 02 November 2003

  • Published: 09 October 2004

  • Issue Date: February 2005

  • DOI: https://doi.org/10.1007/s00440-003-0322-y

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Keywords

  • Stochastic Process
  • Probability Theory
  • Mathematical Biology
  • Significant Part
  • Random Measure
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