Fractionally integrated inverse stable subordinators
  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. 
Alexander Iksanov, Zakhar Kabluchko, Alexander Marynych and Georgiy   Shevchenko
math.PR