On the Distribution of the Product of Independent Beta Random Variables — Applications

2020 ◽  
pp. 85-117
Author(s):  
Carlos A. Coelho ◽  
Rui P. Alberto
Keyword(s):  
Random Variables ◽  
Beta Random Variables

scholarly journals On the law of homogeneous stable functionals

2019 ◽  
Vol 23 ◽  
pp. 82-111
Author(s):  
Julien Letemplier ◽  
Thomas Simon
Keyword(s):  
Random Variables ◽  
Infinite Divisibility ◽  
Explicit Computation ◽  
Infinite Products ◽  
Stable Lévy Process ◽  
Distributional Properties ◽  
Lamperti Transformation ◽  
Beta Random Variables ◽  
Generalized Gamma Convolution ◽  
The Law

LetAbe theLq-functional of a stable Lévy process starting from one and killed when crossing zero. We observe thatAcan be represented as the independent quotient of two infinite products of renormalized Beta random variables. The proof relies on Markovian time change, the Lamperti transformation, and an explicit computation performed in [38] on perpetuities of hypergeometric Lévy processes. This representation allows us to retrieve several factorizations previously shown by various authors, and also to derive new ones. We emphasize the connections betweenAand more standard positive random variables. We also investigate the law of Riemannian integrals of stable subordinators. Finally, we derive several distributional properties ofArelated to infinite divisibility, self-decomposability, and the generalized Gamma convolution.

A Note on the Product of Independent Beta Random Variables

2020 ◽  
pp. 69-83
Author(s):  
Filipe J. Marques ◽  
Indranil Ghosh ◽  
Johan Ferreira ◽  
Andriëtte Bekker
Keyword(s):  
Random Variables ◽  
Beta Random Variables
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