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


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.


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Svante Janson. "Moments of Gamma type and the Brownian supremum process area." Probab. Surveys 7 1 - 52, 2010.


Published: 2010
First available in Project Euclid: 23 April 2010

zbMATH: 1194.60019
MathSciNet: MR2645216
Digital Object Identifier: 10.1214/10-PS160

Primary: 60E10
Secondary: 60J15

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

Rights: Copyright © 2010 The Institute of Mathematical Statistics and the Bernoulli Society

Vol.7 • 2010
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