Fractionally integrated inverse stable subordinators

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• 作者：Alexander Iksanov^a ; ^{iksan@univ.kiev.ua} ; Zakhar Kabluchko^b ; ^{zakhar.kabluchko@uni-muenster.de} ; Alexander Marynych^a ; ^b ; ^{marynych@unicyb.kiev.ua} ; Georgiy Shevchenko^c ; ^{zhora@univ.kiev.ua}
• 关键词：primary ; 60F17 ; 60G17 ; secondary ; 60G18
• 刊名：Stochastic Processes and their Applications
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：127
• 期：1
• 页码：80-106
• 全文大小：460 K
• 卷排序：127

文摘

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.