The integral of the supremum process of Brownian motion
2009 (English)In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 46, no 2, 593-600 p.Article in journal (Refereed) Published
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.
Place, publisher, year, edition, pages
2009. Vol. 46, no 2, 593-600 p.
Brownian motion, supremum process, local time, Brownian areas
IdentifiersURN: urn:nbn:se:uu:diva-98029DOI: 10.1239/jap/1245676109ISI: 000267854000021OAI: oai:DiVA.org:uu-98029DiVA: diva2:173189