Monotone convolution semigroups

Takahiro Hasebe. "Monotone convolution semigroups." Studia Mathematica 200.2 (2010): 175-199. <http://eudml.org/doc/285531>.

@article{TakahiroHasebe2010,
abstract = {We study how a property of a monotone convolution semigroup changes with respect to the time parameter. Especially we focus on "time-independent properties": in the classical case, there are many properties of convolution semigroups (or Lévy processes) which are determined at an instant, and moreover, such properties are often characterized by the drift term and Lévy measure. In this paper we exhibit such properties of monotone convolution semigroups; an example is the concentration of the support of a probability measure on the positive real line. Most of them are characterized by the same conditions on drift terms and Lévy measures as known in probability theory. These kinds of properties are mapped bijectively by a monotone analogue of the Bercovici-Pata bijection. Finally we compare such properties with classical, free, and Boolean cases, which will be important in an approach to unify these notions of independence.},
author = {Takahiro Hasebe},
journal = {Studia Mathematica},
keywords = {monotone independence; monotone convolution; monotone Lévy processes},
language = {eng},
number = {2},
pages = {175-199},
title = {Monotone convolution semigroups},
url = {http://eudml.org/doc/285531},
volume = {200},
year = {2010},
}

TY - JOUR
AU - Takahiro Hasebe
TI - Monotone convolution semigroups
JO - Studia Mathematica
PY - 2010
VL - 200
IS - 2
SP - 175
EP - 199
AB - We study how a property of a monotone convolution semigroup changes with respect to the time parameter. Especially we focus on "time-independent properties": in the classical case, there are many properties of convolution semigroups (or Lévy processes) which are determined at an instant, and moreover, such properties are often characterized by the drift term and Lévy measure. In this paper we exhibit such properties of monotone convolution semigroups; an example is the concentration of the support of a probability measure on the positive real line. Most of them are characterized by the same conditions on drift terms and Lévy measures as known in probability theory. These kinds of properties are mapped bijectively by a monotone analogue of the Bercovici-Pata bijection. Finally we compare such properties with classical, free, and Boolean cases, which will be important in an approach to unify these notions of independence.
LA - eng
KW - monotone independence; monotone convolution; monotone Lévy processes
UR - http://eudml.org/doc/285531
ER -