Fractionally integrated inverse stable subordinators

Alexander Iksanov, Zakhar Kabluchko, Alexander Marynych and Georgiy Shevchenko

Stochastic Processes and their Applications, 2017, vol. 127, issue 1, 80-106

Abstract: 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. 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 Hölder continuity of FIISS and a law of iterated logarithm for both small and large times.

Keywords: Hölder continuity; Inverse stable subordinator; Lamperti representation; Law of iterated logarithm; Renewal shot noise process; Self-similarity; Weak convergence in the Skorokhod space (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1016/j.spa.2016.06.001

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