Hitting times to spheres of Brownian motions with drifts starting from the origin

Proceedings of the Japan Academy, Series A. Mathematical Sciences

article

Yuji Hamana¹ 

[1] Department of Mathematics, Kumamoto University

关键词: Brownian motion with drift;    first hitting time;    modified Bessel functions.;   

DOI  :  10.3792/pjaa.95.37

学科分类：数学（综合）

来源: Japan Academy

【 摘 要 】

We investigate the first hitting times to spheres of Brownian motions with constant drifts. In the case when the Brownian motion starts from a point in $\mathbf{R}^{d}$ except for the origin, an explicit formula for the density function of the hitting time has been obtained. When the starting point is the origin, we represent the density function by means of the density of the hitting time of the Brownian motion without the drift.

【 授权许可】

Unknown