Probability Surveys

Moments of Gamma type and the Brownian supremum process area

Svante Janson

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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.

Article information

Source
Probab. Surveys, Volume 7 (2010), 1-52.

Dates
First available in Project Euclid: 23 April 2010

Permanent link to this document
https://projecteuclid.org/euclid.ps/1272029738

Digital Object Identifier
doi:10.1214/10-PS160

Mathematical Reviews number (MathSciNet)
MR2645216

Zentralblatt MATH identifier
1194.60019

Subjects
Primary: 60E10: Characteristic functions; other transforms
Secondary: 60J15

Keywords
Moments Gamma function Brownian motion supremum process generalized Pólya urns

Citation

Janson, Svante. Moments of Gamma type and the Brownian supremum process area. Probab. Surveys 7 (2010), 1--52. doi:10.1214/10-PS160. https://projecteuclid.org/euclid.ps/1272029738


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See also

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