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Abstract
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.
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Ostrovsky D. A Note on the $S_2(\delta)$ Distribution and the Riemann Xi
Function. ELECTRONIC COMMUNICATIONS IN PROBABILITY 2014. [DOI: 10.1214/ecp.v19-3608] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Ostrovsky D. Theory of Barnes Beta distributions. ELECTRONIC COMMUNICATIONS IN PROBABILITY 2013. [DOI: 10.1214/ecp.v18-2445] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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