NDLI: The Integral of the Supremum Process of Brownian Motion

Content Provider	Scilit
Author	Janson, Svante Petersson, Niclas
Copyright Year	2009
Description	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)(T) covered by the process in the time interval [0,T]. The Laplace transform of(T) follows as a consequence. The main proof involves a double Laplace transform of(T) and is based on excursion theory and local time for Brownian motion.
Related Links	https://www.cambridge.org/core/services/aop-cambridge-core/content/view/94FBFA49F48217DC3F3038D59261464D/S0021900200005672a.pdf/div-class-title-the-integral-of-the-supremum-process-of-brownian-motion-div.pdf
Ending Page	600
Page Count	8
Starting Page	593
ISSN	00219002
e-ISSN	14756072
DOI	10.1017/s0021900200005672
Journal	Journal of applied probability
Issue Number	02
Volume Number	46
Language	English
Publisher	Cambridge University Press (CUP)
Publisher Date	2009-06-01
Access Restriction	Open
Subject Keyword	Journal of applied probability Mathematical Physics Brownian Motion Supremum Process Local Time Brownian Areas
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Statistics, Probability and Uncertainty

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The Integral of the Supremum Process of Brownian Motion