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Numerical computation of hitting time distributions of increasing Lévy processes

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  • Choe, Geon Ho
  • Lee, Dong Min

Abstract

We introduce a method for computation of hitting time distribution of an increasing Lévy process using the inverse Fourier transform and the Hilbert transform under the assumption that the characteristic function of the process is given. Its efficiency is demonstrated by the Kolmogorov–Smirnov test.

Suggested Citation

  • Choe, Geon Ho & Lee, Dong Min, 2016. "Numerical computation of hitting time distributions of increasing Lévy processes," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 289-294.
    • Handle: RePEc:eee:stapro:v:119:y:2016:i:c:p:289-294
    DOI: 10.1016/j.spl.2016.08.013
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    References listed on IDEAS

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    1. Kumar, A. & Vellaisamy, P., 2015. "Inverse tempered stable subordinators," Statistics & Probability Letters, Elsevier, vol. 103(C), pages 134-141.
    2. Küchler, Uwe & Tappe, Stefan, 2013. "Tempered stable distributions and processes," Stochastic Processes and their Applications, Elsevier, vol. 123(12), pages 4256-4293.
    3. Meerschaert, Mark M. & Scheffler, Hans-Peter, 2008. "Triangular array limits for continuous time random walks," Stochastic Processes and their Applications, Elsevier, vol. 118(9), pages 1606-1633, September.
    4. Veillette, Mark & Taqqu, Murad S., 2010. "Using differential equations to obtain joint moments of first-passage times of increasing Lévy processes," Statistics & Probability Letters, Elsevier, vol. 80(7-8), pages 697-705, April.
    5. Meerschaert, Mark M. & Scheffler, Hans-Peter, 2006. "Stochastic model for ultraslow diffusion," Stochastic Processes and their Applications, Elsevier, vol. 116(9), pages 1215-1235, September.
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