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Hitting times to spheres of Brownian motions with drifts starting from the origin. (English) Zbl 07121252
Summary: 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.
MSC:
60J65 Brownian motion
60G40 Stopping times; optimal stopping problems; gambling theory
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