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The joint distribution of the hitting time and place to a sphere or spherical shell for Brownian motion with drift

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  • Yin, Chuancun

Abstract

Let Xt be a standard d-dimensional Brownian motion with drift c started at a fixed X0, 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 XT is determined.

Suggested Citation

  • Yin, Chuancun, 1999. "The joint distribution of the hitting time and place to a sphere or spherical shell for Brownian motion with drift," Statistics & Probability Letters, Elsevier, vol. 42(4), pages 367-373, May.
    • Handle: RePEc:eee:stapro:v:42:y:1999:i:4:p:367-373
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    Cited by:

    1. Gzyl, Henryk & ter Horst, Enrique & Villasana, Minaya, 2015. "Numerical determination of hitting time distributions from their Laplace transforms: One dimensional diffusions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 594-602.
    2. Atkinson, Michael P. & Singham, Dashi I., 2015. "Multidimensional hitting time results for Brownian bridges with moving hyperplanar boundaries," Statistics & Probability Letters, Elsevier, vol. 100(C), pages 85-92.

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