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

被引：2

作者：

Bridaa, Safa ^{[1
]}

Jedidi, Wissem ^{[2
]}

Sendov, Hristo ^{[3
]}

机构：

[1] Univ Tunis El Manar, Fac Sci Tunis, Dept Math, Lab Anal Math & Applicat LR11ES11, Tunis 2092, Tunisia

[2] King Saud Univ, Dept Stat & Operat Res, POB 2455, Riyadh 11451, Saudi Arabia

[3] Univ Western Ontario, Dept Stat & Actuarial Sci, London, ON N6A 5B7, Canada

来源：

JOURNAL OF THEORETICAL PROBABILITY | 2024年 / 37卷 / 01期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Bernstein function; Complete monotonicity; Generalized unimodality; Mittag-Leffler function; Positive stable distribution; Subordinators;

D O I：

10.1007/s10959-023-01242-z

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Using the differential operator Omega(s) := s I - xd/dx, 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.

引用

页码：1 / 42

页数：42

共 18 条

[1] Bertoin J., 1999, Lectures on Probability Theory and Statistics, DOI [10.1214/ECP.v6-1039, DOI 10.1214/ECP.V6-1039]
[2] BONDESSON L, 1992, LECT NOTES STAT, V76
[3] Carter M., 2000, Undergraduate Texts in Mathematics, DOI [10.1007/978-1-4612-1174-7, DOI 10.1007/978-1-4612-1174-7]
[4] Chaumont L, 2012, CAMBRIDGE SERIES STA, V2
[5] Gorenflo R., 2020, Mittag-Leffler Functions, Related Topics and Applications, DOI [10.1007/ 978-3-662-43930-2, DOI 10.1007/978-3-662-43930-2]
[6] Hansen B., 1989, J PROPUL POWER, V89-08, P1
[7] Generalized Gamma Convolutions, Dirichlet means, Thorin measures, with explicit examples
James, Lancelot F.
Roynette, Bernard
Yor, Marc
[J]. PROBABILITY SURVEYS, 2008, 5 : 346 - 415
[8] STABLE PROCESSES, MIXING, AND DISTRIBUTIONAL PROPERTIES. II
Jedidi, W.
[J]. THEORY OF PROBABILITY AND ITS APPLICATIONS, 2009, 53 (01) : 81 - 105
[9] Three classes of decomposable distributions
Jedidi, Wissem
Basalim, Kholoud
Bridaa, Safa
[J]. OPEN MATHEMATICS, 2020, 18 : 1855 - 1878
[10] Kyprianou A.E., 2006, INTRO LECT

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