Three classes of decomposable distributions-Reference-Cited by-同舟云学术

Three classes of decomposable distributions

Published:2020-01-01 Issue:1 Volume:18 Page:1855-1878
ISSN:2391-5455
Container-title:Open Mathematics
language:en
Short-container-title:

Author:

Jedidi Wissem¹,Basalim Kholoud¹,Bridaa Safa²

Affiliation:

1. King Saud University, Department of Statistics & OR, College of Sciences , Riyadh 11451 , Kingdom of Saudi Arabia

2. Université de Tunis El Manar, Faculté des Sciences de Tunis, Laboratoire d’Analyse Mathématiques et Applications LR11ES11 , 2092 , Tunis , Tunisia

Abstract

Abstract In this work, we refine the results of Sendov and Shan [New representation theorems for completely monotone and Bernstein functions with convexity properties on their measures, J. Theor. Probab. 28 (2015), 1689–1725] on subordinators obtained by the class of Bernstein functions stable by the Mellin-Euler differential operator

I − x d d x

I-x\tfrac{\text{d}}{\text{d}x}

by giving a stochastic interpretation, proving monotonicity properties of the related distributions and providing additional extensions.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/math-2020-0124/pdf

Reference15 articles.

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2. R. L. Schilling , R. Song , and Z. Vondraček , Bernstein Functions. Theory and Applications, 2 edn., De Gruyter Studies in Mathematics 37 , Walter de Gruyter & Co., Berlin, 2012.

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4. L. Steutel and K. Van Harn , Infinite Divisibility of Probability Distributions on the Real Line, Marcel Dekker, New York, Basel, 2004.

5. A. E. Kyprianou , Fluctuations of Lévy Processes with Applications, Introductory Lectures, 2 edn., Springer-Verlag, Berlin Heidelberg, 2006.

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