An algebra of Stein operators

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:469

Article

Gaunt, Robert E.¹  Mijoule, Guillaume²  Swan, Yvik³ 

[1] Univ Manchester, Sch Math, Manchester M13 9PL, Lancs, England

[2] INRIA Paris, MOKAPLAN, 2 Rue Simone Iff,CS 42112, F-75589 Paris 12, France

[3] Univ Liege, Allee Decouverte 12, B-8000 Liege, Belgium

关键词: Stein's method;    Stein operators;    Product distributions;    Variance-gamma distribution;   

DOI  :  10.1016/j.jmaa.2018.09.015

来源: Elsevier

【 摘 要 】

We build upon recent advances on the distributional aspect of Stein's method to propose a novel and flexible technique for computing Stein operators for random variables that can be written as products of independent random variables. We show that our results are valid for a wide class of distributions including normal, beta, variance-gamma, generalized gamma and many more. Our operators are kth degree differential operators with polynomial coefficients; they are straightforward to obtain even when the target density bears no explicit handle. As an application, we derive a new formula for the density of the product of k independent symmetric variance-gamma distributed random variables. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free