RESEARCH ARTICLE


Hitting Time and Place of Brownian Motion with Drift



Chuancun Yin, Chunwei Wang*
School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China.


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© 2009 Yin et al.;

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: https://creativecommons.org/licenses/by/4.0/legalcode. This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China. E-mail: ccyin@mail.qfnu.edu.cn


Abstract

We consider a d-dimensional Brownian motion in Rd with drift. The explicit expressions are obtained for the joint density of the hitting time and place to a sphere, when the process starts either from the inside the sphere or from the out of sphere.

Keywords: Brownian motion with drift, hitting time, hitting place, Joint density..