Proceedings of the Japan Academy, Series A, Mathematical Sciences

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

Yuji Hamana

Full-text: Open access

Abstract

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

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

Dates
First available in Project Euclid: 1 April 2019

Permanent link to this document
https://projecteuclid.org/euclid.pja/1554084023

Digital Object Identifier
doi:10.3792/pjaa.95.37

Mathematical Reviews number (MathSciNet)
MR3934984

Zentralblatt MATH identifier
07121252

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

Keywords
Brownian motion with drift first hitting time modified Bessel functions

Citation

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. https://projecteuclid.org/euclid.pja/1554084023


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