Proceedings of the Japan Academy, Series A, Mathematical Sciences

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

Yuji Hamana

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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.

Article information

Proc. Japan Acad. Ser. A Math. Sci., Volume 95, Number 4 (2019), 37-39.

First available in Project Euclid: 1 April 2019

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Mathematical Reviews number (MathSciNet)

Primary: 60J65: Brownian motion [See also 58J65]
Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]

Brownian motion with drift first hitting time modified Bessel functions


Hamana, Yuji. Hitting times to spheres of Brownian motions with drifts starting from the origin. Proc. Japan Acad. Ser. A Math. Sci. 95 (2019), no. 4, 37--39. doi:10.3792/pjaa.95.37.

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