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 Probability Surveys > Vol. 7 (2010) open journal systems 


Moments of Gamma type and the Brownian supremum process area

Svante Janson, Uppsala University


Abstract
We study positive random variables whose moments can be expressed by products and quotients of Gamma functions; this includes many standard distributions. General results are given on existence, series expansion and asymptotics of density functions. It is shown that the integral of the supremum process of Brownian motion has moments of this type, as well as a related random variable occurring in the study of hashing with linear displacement, and the general results are applied to these variables.

Addendum: An addendum is published in Probability Surveys 7 (2010) 207–208.

AMS 2000 subject classifications: Primary 60E10; secondary 60J15.

Keywords: Moments, Gamma function, Brownian motion, supremum process, generalized Pólya urns.

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Janson, Svante, Moments of Gamma type and the Brownian supremum process area, Probability Surveys, 7, (2010), 1-52 (electronic). DOI: 10.1214/10-PS160.

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Probability Surveys. ISSN: 1549-5787