The tail of the maximum of Brownian motion minus a parabola

Details The tail of the maximum of Brownian motion minus a parabola The tail of the maximum of Brownian motion minus a parabola

2010-11-17

arxiv.org/abs/1011.3972v3

Mathematics

Probability

12 pages, submitted to the Electronic Communications in Probability

Scientific paper

We analyze the tail behavior of the maximum N of Brownian motion minus a parabola and give an asymptotic expansion for P(N>x) as x tends to infinity. This extends a first order result on the tail behavior, which can be deduced from Huesler and Piterbarg (1999). We also point out the relation between certain results in Groeneboom (2010) and Janson, Louchard and Martin-L\"of (2010).

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