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Teoriya Veroyatnostei i ee Primeneniya, 2025, Volume 70, Issue 1, Pages 88–110
DOI: https://doi.org/10.4213/tvp5648 (Mi tvp5648) 		 
Lévy processes with jumps governed by lower incomplete gamma subordinator and its variations

M. S. Babulala, S. K. Gauttama, Maheshwarib

a Department of Mathematics, The LNM Institute of Information Technology, Jaipur, Rajasthan, India
b Operations Management and Quantitative Techniques Area, Indian Institute of Management Indore, Indore, Madhya Pradesh, India
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DOI: https://doi.org/10.4213/tvp5648
Abstract: In this paper, we study the Lévy process time-changed by independent Lévy subordinators, namely, the incomplete gamma subordinator, the $\varepsilon$-jumps incomplete gamma subordinator, and tempered incomplete gamma subordinator. We derive their important distributional properties such as mean, variance, correlation, tail probabilities, and fractional moments. The long-range dependence property of these processes is discussed. An application in the insurance domain is studied in detail. Finally, we present the simulated sample paths for the subordinators.
Keywords: incomplete gamma function, Lévy subordinator, compound Poisson process.
Funding agency Grant number
Fund for Improvement of S&T infrastructure in universities & higher educational institutions (FIST) SR/FST/MS-I/2018/24
First author acknowledges the Centre for Mathematical & Financial Computing and the DST-FIST grant for the infrastructure support for the computing lab facility under the scheme FIST (File No: SR/FST/MS-I/2018/24) at the LNMIIT, Jaipur.
Received: 14.04.2023
Revised: 21.12.2023
Accepted: 15.01.2024
Published: 27.01.2025
English version:
Theory of Probability and its Applications, 2025, Volume 70, Issue 1, Pages 73–91
DOI: https://doi.org/10.1137/S0040585X97T992240
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: M. S. Babulal, S. K. Gauttam, Maheshwari, “Lévy processes with jumps governed by lower incomplete gamma subordinator and its variations”, Teor. Veroyatnost. i Primenen., 70:1 (2025), 88–110; Theory Probab. Appl., 70:1 (2025), 73–91
Citation in format AMSBIB
\Bibitem{BabGauMah25}
\by M.~S.~Babulal, S.~K.~Gauttam, Maheshwari
\paper L\'evy processes with jumps governed by lower incomplete gamma subordinator and its variations
\jour Teor. Veroyatnost. i Primenen.
\yr 2025
\vol 70
\issue 1
\pages 88--110
\mathnet{http://mi.mathnet.ru/tvp5648}
\crossref{https://doi.org/10.4213/tvp5648}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=4856749}
\transl
\jour Theory Probab. Appl.
\yr 2025
\vol 70
\issue 1
\pages 73--91
\crossref{https://doi.org/10.1137/S0040585X97T992240}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-105005890451}
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