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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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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DOI: https://doi.org/10.1007/s00440-003-0322-y
Keywords
- Stochastic Process
- Probability Theory
- Mathematical Biology
- Significant Part
- Random Measure