@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",
}
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 -
