Fractionally integrated inverse stable subordinators
Probability
2016-02-25 v1
Abstract
A fractionally integrated inverse stable subordinator (FIISS) is the convolution of a power function and an inverse stable subordinator. We show that the FIISS is a scaling limit in the Skorokhod space of a renewal shot noise process with heavy-tailed, infinite mean `inter-shot' distribution and regularly varying response function. We prove local H\"{o}lder continuity of FIISS and a law of iterated logarithm for both small and large times.
Cite
@article{arxiv.1602.07485,
title = {Fractionally integrated inverse stable subordinators},
author = {Alexander Iksanov and Zakhar Kabluchko and Alexander Marynych and Georgiy Shevchenko},
journal= {arXiv preprint arXiv:1602.07485},
year = {2016}
}
Comments
7 figures