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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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