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2011 The tail of the maximum of Brownian motion minus a parabola
Piet Groeneboom, Nico Temme
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Electron. Commun. Probab. 16: 458-466 (2011). DOI: 10.1214/ECP.v16-1645

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).

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Piet Groeneboom. Nico Temme. "The tail of the maximum of Brownian motion minus a parabola." Electron. Commun. Probab. 16 458 - 466, 2011. https://doi.org/10.1214/ECP.v16-1645

Information

Accepted: 24 August 2011; Published: 2011
First available in Project Euclid: 7 June 2016

zbMATH: 1244.60052
MathSciNet: MR2831084
Digital Object Identifier: 10.1214/ECP.v16-1645

Subjects:
Primary: 60J65
Secondary: 60J75

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