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Inverse tempered stable subordinators

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  • Kumar, A.
  • Vellaisamy, P.

Abstract

We consider the first-exit time of a tempered β-stable subordinator, also called inverse tempered stable (ITS) subordinator. An integral form representation and a series representation for the density of the ITS subordinator are obtained. The asymptotic behavior of the q-th order moments of the ITS subordinator are investigated. The limiting form of the ITS density and its k-th order derivatives are derived as the space variable x→0+. Finally, the governing pde of the ITS density is also obtained.

Suggested Citation

  • Kumar, A. & Vellaisamy, P., 2015. "Inverse tempered stable subordinators," Statistics & Probability Letters, Elsevier, vol. 103(C), pages 134-141.
    • Handle: RePEc:eee:stapro:v:103:y:2015:i:c:p:134-141
    DOI: 10.1016/j.spl.2015.04.010
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. A. Maheshwari & P. Vellaisamy, 2019. "Fractional Poisson Process Time-Changed by Lévy Subordinator and Its Inverse," Journal of Theoretical Probability, Springer, vol. 32(3), pages 1278-1305, September.
    2. Gajda, J. & Kumar, A. & Wyłomańska, A., 2019. "Stable Lévy process delayed by tempered stable subordinator," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 284-292.
    3. Giacomo Ascione & Nikolai Leonenko & Enrica Pirozzi, 2022. "Non-local Solvable Birth–Death Processes," Journal of Theoretical Probability, Springer, vol. 35(2), pages 1284-1323, June.
    4. Torricelli, Lorenzo, 2020. "Trade duration risk in subdiffusive financial models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
    5. Kumar, A. & Wyłomańska, A. & Połoczański, R. & Sundar, S., 2017. "Fractional Brownian motion time-changed by gamma and inverse gamma process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 648-667.
    6. Gupta, Neha & Kumar, Arun, 2022. "Inverse tempered stable subordinators and related processes with Mellin transform," Statistics & Probability Letters, Elsevier, vol. 186(C).
    7. Shantanu Awasthi & Indranil SenGupta, 2020. "First exit-time analysis for an approximate Barndorff-Nielsen and Shephard model with stationary self-decomposable variance process," Papers 2006.07167, arXiv.org, revised Jan 2021.
    8. 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.
    9. A. Kumar & J. Gajda & A. Wyłomańska & R. Połoczański, 2019. "Fractional Brownian Motion Delayed by Tempered and Inverse Tempered Stable Subordinators," Methodology and Computing in Applied Probability, Springer, vol. 21(1), pages 185-202, March.

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