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Generalized Unimodality and Subordinators, With Applications to Stable Laws and to the Mittag-Leffler Function

Author

Listed:
  • Safa Bridaa

    (Université de Tunis El Manar)

  • Wissem Jedidi

    (King Saud University)

  • Hristo Sendov

    (University of Western Ontario)

Abstract

Using the differential operator $$\Omega _s:=s\;I- x \frac{\textrm{d}}{\textrm{d}x}, \; s>0$$ Ω s : = s I - x d d x , s > 0 , we build a new class of infinitely divisible distributions on the half-line. For this class, we give a stochastic interpretation and we provide several monotonicity properties for the associated subordinators. As an application, we solve a problem raised separately by Sendov and Shan in (J Theor Probab 28:1689–1725, 2015) and by Simon in (Math Nachr 285(4): 497–506, 2012) on the distribution of the stable subordinators. Finally, we provide a new complete monotonicity property for the Mittag-Leffler function.

Suggested Citation

  • Safa Bridaa & Wissem Jedidi & Hristo Sendov, 2024. "Generalized Unimodality and Subordinators, With Applications to Stable Laws and to the Mittag-Leffler Function," Journal of Theoretical Probability, Springer, vol. 37(1), pages 1-42, March.
    • Handle: RePEc:spr:jotpro:v:37:y:2024:i:1:d:10.1007_s10959-023-01242-z
    DOI: 10.1007/s10959-023-01242-z
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