Monotone convolution semigroups

• Autorzy: Takahiro Hasebe
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46L53: Noncommutative probability and statistics
• 46L54: Free probability and free operator algebras
• 34A25: Analytical theory: series, transformations, transforms, operational calculus, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2010
• Tom: 200
• Numer: 2
• Strony: 175-199

Daty

wydano

2010

Twórcy

autor

Takahiro Hasebe

• Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan

Identyfikatory

DOI

10.4064/sm200-2-5