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Inverse tempered stable subordinators and related processes with Mellin transform

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  • Gupta, Neha
  • Kumar, Arun

Abstract

In this article, the infinite series form of the probability densities of tempered stable and inverse tempered stable subordinators are obtained using Mellin transform. Further, the densities of the products and quotients of stable and inverse stable subordinators are worked out. The asymptotic behaviors of these densities are obtained as x→0+. Similar results for tempered and inverse tempered stable subordinators are discussed. Our results provide alternative methods to find the densities of these subordinators and complement the results available in literature.

Suggested Citation

  • Gupta, Neha & Kumar, Arun, 2022. "Inverse tempered stable subordinators and related processes with Mellin transform," Statistics & Probability Letters, Elsevier, vol. 186(C).
    • Handle: RePEc:eee:stapro:v:186:y:2022:i:c:s016771522200058x
    DOI: 10.1016/j.spl.2022.109465
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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.
    2. Kumar, A. & Vellaisamy, P., 2015. "Inverse tempered stable subordinators," Statistics & Probability Letters, Elsevier, vol. 103(C), pages 134-141.
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