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The joint distribution of the hitting time and place to a sphere or spherical shell for Brownian motion with drift. (English) Zbl 0945.60087
Summary: Let $$X_t$$ be a standard $$d$$-dimensional Brownian motion with drift $$c$$ started at a fixed $$X_0$$, and let $$T$$ be the hitting time for a sphere or concentric spherical shell. By using an appropriate martingale, a Laplace-Gegenbauer transform of the joint distribution of $$T$$ and $$X_T$$ is determined.

##### MSC:
 60J65 Brownian motion
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##### References:
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