##
Alexander M. Iksanov

Fractionally integrated inverse stable subordinators

### Résumé

A fractionally integrated inverse stable subordinator
(FIISS) is the convolution of an inverse stable subordinator, also known
as a Mittag-Leffler process, and a power function. I am going to discuss
various path properties of FIISS including Hoelder continuity and
laws of iterated logarithm and several distributional properties of FIISS
such as self-similarity and tail behavior. I will explain that the FIISS is a
quite natural probabilistic object, for it arises as a functional weak
limit for appropriate shot noise processes. The talk is based on a recent
joint paper with Z. Kabluchko, A. Marynych, G. Shevchenko (SPA, V. 127
(2017), 80-106).