On monotone convolution and monotone infinite divisivility

Details On monotone convolution and monotone infinite divisivility On monotone convolution and monotone infinite divisivility

2010-02-18

arxiv.org/abs/1002.3430v2

Mathematics

Operator Algebras

This is master's thesis of the author (with revision) in Kyoto University, 2009. A part of this paper was published in Infin.

Scientific paper

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.

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