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Generalized continuous time random walks and Hermite processes

Author

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  • Chen, Zhenlong
  • Xu, Lin
  • Zhu, Dongjin

Abstract

Generalized continuous time random walks with independent, heavy-tailed random waiting times and long range dependent jumps are considered. Their scaling limits are determined in terms of the Hermite processes and inverse of stable subordinators. These limiting processes provide an interesting new class of non-Markovian, non-Gaussian self-similar processes.

Suggested Citation

  • Chen, Zhenlong & Xu, Lin & Zhu, Dongjin, 2015. "Generalized continuous time random walks and Hermite processes," Statistics & Probability Letters, Elsevier, vol. 99(C), pages 44-53.
    • Handle: RePEc:eee:stapro:v:99:y:2015:i:c:p:44-53
    DOI: 10.1016/j.spl.2014.12.027
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    References listed on IDEAS

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    1. Meerschaert, Mark M. & Nane, Erkan & Xiao, Yimin, 2009. "Correlated continuous time random walks," Statistics & Probability Letters, Elsevier, vol. 79(9), pages 1194-1202, May.
    2. Albin, J. M. P., 1998. "A note on Rosenblatt distributions," Statistics & Probability Letters, Elsevier, vol. 40(1), pages 83-91, September.
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    Cited by:

    1. Stoyan V. Stoyanov & Yong Shin Kim & Svetlozar T. Rachev & Frank J. Fabozzi, 2017. "Option pricing for Informed Traders," Papers 1711.09445, arXiv.org.
    2. Stoyan V. Stoyanov & Svetlozar T. Rachev & Stefan Mittnik & Frank J. Fabozzi, 2019. "Pricing Derivatives In Hermite Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(06), pages 1-27, September.

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