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The tail of the maximum of Brownian motion minus a parabola


 
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1. Title Title of document The tail of the maximum of Brownian motion minus a parabola
 
2. Creator Author's name, affiliation, country Piet Groeneboom; Delft University of Technology
 
2. Creator Author's name, affiliation, country Nico M. Temme; CWI
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Brownian motion, parabolic drift, maximum, Airy functions
 
3. Subject Subject classification 60J65,60J75
 
4. Description Abstract We analyze the tail behavior of the maximum $N$ of $\{W(t)-t^2:t\ge0\}$, where $W$ is standard Brownian motion on $[0,\infty)$, and give an asymptotic expansion for ${\mathbb P}\{N\ge x\}$, as $x\to\infty$. This extends a first order result on the tail behavior, which can be deduced from Hüsler and Piterbarg (1999). We also point out the relation between certain results in Janson et al. (2010) and Groeneboom (2010).
 
5. Publisher Organizing agency, location
 
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7. Date (YYYY-MM-DD) 2011-08-24
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/1645
 
10. Identifier Digital Object Identifier 10.1214/ECP.v16-1645
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 16
 
12. Language English=en
 
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