Hitting Spheres with Brownian Motion and Sommerfeld′s Radiation Condition

Hitting Time and Place of Brownian Motion with Drift

We consider a d-dimensional Brownian motion in d 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.

Hitting a Boundary Point with Reflected Brownian Motion

An explicit integral test involving the reflection angle is given for the reflected Brownian motion in a half-plane to hit a fixed boundary point.

Simultaneous boundary hitting for a two point reflecting brownian motion

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The hitting time density for a reflected Brownian motion

Reflected Brownian motion has been played an important role in economics, finance, queueing and many other fields. In this paper, we present the explicit spectral representation for the hitting time density of the reflected Brownian motion with two-sided barriers, and give some detailed analysis on the computational issues. Numerical analysis reveals that the spectral representation is more app...

Hitting probabilities for Brownian motion on Riemannian manifolds