On monotone convolution and monotone infinite divisivility
arXiv:1002.3430
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 Lévy processes hold such as characterizations of subordinators and strictly stable distributions.
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