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

Safa Bridaa (), Wissem Jedidi () and Hristo Sendov ()
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Safa Bridaa: Université de Tunis El Manar
Wissem Jedidi: King Saud University
Hristo Sendov: University of Western Ontario

Journal of Theoretical Probability, 2024, vol. 37, issue 1, 1-42

Abstract: 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.

Keywords: Bernstein function; Complete monotonicity; Generalized unimodality; Mittag-Leffler function; Positive stable distribution; Subordinators; Primary 26A48; 26D07; Secondary 30E20 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10959-023-01242-z

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