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).