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Steen Thorbjørnsen

The Lévy-Itô decomposition in free probability

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The Lévy-Itô decomposition in free probability. / Barndorff-Nielsen, Ole Eiler; Thorbjørnsen, Steen.

In: Prob. Theory Rel. Fields, Vol. 131, No. 2, 2005, p. 197-228.

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Barndorff-Nielsen, Ole Eiler ; Thorbjørnsen, Steen. / The Lévy-Itô decomposition in free probability. In: Prob. Theory Rel. Fields. 2005 ; Vol. 131, No. 2. pp. 197-228.

Bibtex

@article{1a567290e5fa11dc9afb000ea68e967b,
title = "The L{\'e}vy-It{\^o} decomposition in free probability",
abstract = "In this paper we prove the free analog of the L{\'e}vy-It{\^o} decomposition for L{\'e}vy 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 L{\'e}vy-It{\^o} decomposition, an alternative proof of the general existence of free L{\'e}vy processes (in law).",
author = "Barndorff-Nielsen, {Ole Eiler} and Steen Thorbj{\o}rnsen",
year = "2005",
doi = "10.1007/s00440-003-0322-y",
language = "English",
volume = "131",
pages = "197--228",
journal = "Prob. Theory Rel. Fields",
number = "2",

}

RIS

TY - JOUR

T1 - The Lévy-Itô decomposition in free probability

AU - Barndorff-Nielsen, Ole Eiler

AU - Thorbjørnsen, Steen

PY - 2005

Y1 - 2005

N2 - 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).

AB - 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).

U2 - 10.1007/s00440-003-0322-y

DO - 10.1007/s00440-003-0322-y

M3 - Journal article

VL - 131

SP - 197

EP - 228

JO - Prob. Theory Rel. Fields

JF - Prob. Theory Rel. Fields

IS - 2

ER -