On monotone convolution and monotone infinite divisivility
Operator Algebras
2010-08-30 v2 Probability
Abstract
This article focuses on properties of monotone convolutions. A criterion for infinite divisibility and time evolution of convolution semigroups are mainly studied. In particular, we clarify that many analogues of the classical results of L\'{e}vy processes hold such as characterizations of subordinators and strictly stable distributions.
Cite
@article{arxiv.1002.3430,
title = {On monotone convolution and monotone infinite divisivility},
author = {Takahiro Hasebe},
journal= {arXiv preprint arXiv:1002.3430},
year = {2010}
}
Comments
This is master's thesis of the author (with revision) in Kyoto University, 2009. A part of this paper was published in Infin. Dim. Anal. Quantum Probab. Relat. Topics 13 (2010), no. 1, 111-131. Another part will be appear in Studia Math