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Fractionally integrated inverse stable subordinators

Author

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  • Iksanov, Alexander
  • Kabluchko, Zakhar
  • Marynych, Alexander
  • Shevchenko, Georgiy

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.

Suggested Citation

  • Iksanov, Alexander & Kabluchko, Zakhar & Marynych, Alexander & Shevchenko, Georgiy, 2017. "Fractionally integrated inverse stable subordinators," Stochastic Processes and their Applications, Elsevier, vol. 127(1), pages 80-106.
    • Handle: RePEc:eee:spapps:v:127:y:2017:i:1:p:80-106
    DOI: 10.1016/j.spa.2016.06.001
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    References listed on IDEAS

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    1. Iksanov, Alexander & Kabluchko, Zakhar & Marynych, Alexander, 2016. "Weak convergence of renewal shot noise processes in the case of slowly varying normalization," Statistics & Probability Letters, Elsevier, vol. 114(C), pages 67-77.
    2. Iksanov, Alexander, 2013. "Functional limit theorems for renewal shot noise processes with increasing response functions," Stochastic Processes and their Applications, Elsevier, vol. 123(6), pages 1987-2010.
    3. Nane, Erkan, 2009. "Laws of the iterated logarithm for a class of iterated processes," Statistics & Probability Letters, Elsevier, vol. 79(16), pages 1744-1751, August.
    4. Scalas, Enrico & Viles, Noèlia, 2014. "A functional limit theorem for stochastic integrals driven by a time-changed symmetric α-stable Lévy process," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 385-410.
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