Fractionally integrated inverse stable subordinators

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:127

Article

Iksanov, Alexander¹  Kabluchko, Zakhar²  Marynych, Alexander^1,2  Shevchenko, Georgiy³ 

[1] Taras Shevchenko Natl Univ Kyiv, Fac Cybernet, UA-01601 Kiev, Ukraine

[2] Westfal Wilhelms Univ Munster, Inst Math Stat, D-48149 Munster, Germany

[3] Taras Shevchenko Natl Univ Kyiv, Fac Mech & Math, UA-01601 Kiev, Ukraine

关键词: Holder continuity;    Inverse stable subordinator;    Lamperti representation;    Law of iterated logarithm;    Renewal shot noise process;    Self-similarity;    Weak convergence in the Skorokhod space;   

DOI  :  10.1016/j.spa.2016.06.001

来源: Elsevier

【 摘 要 】

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 Holder continuity of FIISS and a law of iterated logarithm for both small and large times. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free