Fractionally integrated inverse stable subordinators

2016/02/24 by Alexander Iksanov, Iksanov, Alexander, Zakhar Kabluchko +5
Mathematics · #60G17 #FOS: Mathematics #Primary: 60F17 #Probability (math.PR) #Secondary: 60G18 #math.PR #msc:60F17 #msc:60G17 #msc:60G18

paper · pdf · doi:10.48550/arxiv.1602.07485

7 figures

arxiv created 2016/02/24 · arxiv updated 2016/02/25

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

Related

• Functional limit theorems for renewal shot noise processes with increasing response functions
• Limit theorems for renewal shot noise processes with decreasing response functions
• Fractionally Integrated Moving Average Stable Processes With Long-Range Dependence
• Inverse Tempered Stable Subordinators
• Scaling limit results for the sum of many inverse Lévy subordinators