Infinite divisibility of interpolated gamma powers

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:405

Article

Privault, Nicolas¹  Yang, Dichuan² 

[1] Nanyang Technol Univ, Sch Phys & Math Sci, Div Math Sci, Singapore 637371, Singapore

[2] City Univ Hong Kong, Dept Math, Kowloon Tong, Hong Kong, Peoples R China

关键词: Infinite divisibility;    Complete monotonicity;    Gamma distribution;    Generalized gamma convolutions;    Powers of random variables;   

DOI  :  10.1016/j.jmaa.2013.03.066

来源: Elsevier

【 摘 要 】

This paper is concerned with the distribution properties of the binomial aX + bX(alpha), where X is a gamma random variable. We show in particular that aX + bX(alpha) is infinitely divisible for all alpha is an element of [1, 2] and a, b is an element of R+, and that for alpha = 2 the second order polynomial aX + bX(2) is a generalized gamma convolution whose Thorin density and Wiener-gamma integral representation are computed explicitly. As a byproduct we deduce that fourth order multiple Wiener integrals are in general not infinitely divisible. (c) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free