The integral of the supremum process of Brownian motion
Svante Janson and Niclas Petersson
Source: J. Appl. Probab.
Volume 46, Number 2
(2009), 593-600.
Abstract
In this paper we study the integral of the supremum process of standard Brownian
motion. We present an explicit formula for the moments of the integral (or area)
𝓐(T) covered by the process in the time interval [0,T]. The
Laplace transform of 𝓐(T) follows as a consequence. The main proof
involves a double Laplace transform of 𝓐(T) and is based on excursion
theory and local time for Brownian motion.
Primary Subjects: 60J65
Secondary Subjects: 60J55
Keywords: Brownian motion; supremum process; local time; Brownian areas
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.jap/1245676109
Digital Object Identifier: doi:10.1239/jap/1245676109
Zentralblatt MATH identifier:
05578828
Mathematical Reviews number (MathSciNet):
MR2535835
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