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arXiv · 1602.07485

Fractionally integrated inverse stable subordinators

Alexander Iksanov·Zakhar Kabluchko·Alexander Marynych·Georgiy Shevchenko
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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.

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Alexander Iksanov, Zakhar Kabluchko, Alexander Marynych, Georgiy Shevchenko. 2016-02-24. Fractionally integrated inverse stable subordinators. https://arxiv.org/abs/1602.07485

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