Conference Agenda

A quasi-infinitely divisible distribution is a probability distribution whose characteristic function can be written as the quotient of the characteristic functions of two infinitely divisible distributions. Equivalently, a probability distribution is quasi-infinitely divisible if and only if its characteristic function admits a Lèvy-Khintchine representation with a signed Lévy measure. In this talk we give some examples of quasi-infinitely divisible distributions and study some of their properties. The talk is based on joint works with David Berger, Merve Kutlu, Lei Pan and Ken-iti Sato.

The set of infinitely divisible distributions in the space of all probability measures is a well studied object in stochastics. In this talk we discuss the divisibility property of quasi-infinitely divisible distribution and prove that not every quasi-infinitely divisible distribution is divisible even in the set of (regular) bounded complex-valued measures. Furthermore, we extend the notion of quasi-infinitely divisible distributions by extending the abelian monoid of probability measures to the Grothendieck group and show that the constructed group is divisible.