On hitting times of affine boundaries by reflecting Brownian motion and Bessel processes

被引：0
作者：
Paavo Salminen
Marc Yor
机构：
[1] Åbo Akademi University,Mathematical Department
[2] Université Pierre et Marie Curie,Laboratoire de Probabilités et Modèles aléatoires
来源：
Periodica Mathematica Hungarica | 2011年 / 62卷
关键词：
reflecting Brownian motion; Bessel process; hitting time; linear boundary; time reversal; time inversion; Brownian bridge; Bessel bridge; 60J65; 60J60;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Firstly, we compute the distribution function for the hitting time of a linear time-dependent boundary t ↦ a + bt, a ≥ 0, b ∈ ℝ, by a reflecting Brownian motion. The main tool hereby is Doob’s formula which gives the probability that Brownian motion started inside a wedge does not hit this wedge. Other key ingredients are the time inversion property of Brownian motion and the time reversal property of diffusion bridges. Secondly, this methodology can also be applied for the three-dimensional Bessel process. Thirdly, we consider Bessel bridges from 0 to 0 with dimension parameter δ > 0 and show that the probability that such a Bessel bridge crosses an affine boundary is equal to the probability that this Bessel bridge stays below some fixed value.
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页码：75 / 101
页数：26
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