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Hitting times to spheres of Brownian motions with and without drifts

Explicit formulae for the densities of the first hitting times to the sphere of Brownian motions with drifts are given. We need to consider the joint distributions of the first hitting times to the sphere and the hitting positions of the standard Brownian motion and explicit expression for their Laplace transforms are given, which are different from the known formulae in the literature and are of independnt interest.

preprint2015arXivOpen access
Yuji HamanaHiroyuki Matsumoto
math.PR
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Yuji HamanaHiroyuki Matsumoto

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