Moments of gamma type and the Brownian supremum process area. (English) Zbl 1194.60019

Janson, Svante

Probab. Surv. 7, 1-52 (2010); addendum ibid. 7, 207-208 (2010).

Summary: 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 a 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.

MSC:

60E10	Characteristic functions; other transforms
60J65	Brownian motion
60G70	Extreme value theory; extremal stochastic processes

Keywords:

moments; gamma function; Brownian motion; supremum process; generalized Pólya urns