2007/07/06 by Svante Janson, Janson, Svante, Niclas Petersson +1
Mathematics · #60J55 #60J65 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60J55 #msc:60J65
paper · pdf · doi:10.48550/arxiv.0707.0989
9 pages, 1 figure
arxiv created 2007/07/06 · arxiv updated 2009/12/01
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.