Summary
Let B be a ball in Rd and X = {Xt,t ≥ 0} be the standard Brownian motion in Rd. Define τB = inf{t > 0: Xt ∉B}, the first exit time of X from the ball. We compute explicitly the transition density function of the killed Brownian motion Xo = {Xt, t < τB} and the joint distribution of (τB,X(τB)}. A result of Wendel [5] is deduced as a simple consequence of the explicit joint density function.
Work supported in part by the grant NSF-MCS-82-01599
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© 1986 Birkhäuser Boston, Inc.
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Hsu, P. (1986). Brownian Exit Distribution of a Ball. In: Çinlar, E., Chung, K.L., Getoor, R.K., Glover, J. (eds) Seminar on Stochastic Processes, 1985. Progress in Probability and Statistics, vol 12. Birkhäuser Boston. https://doi.org/10.1007/978-1-4684-6748-2_8
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DOI: https://doi.org/10.1007/978-1-4684-6748-2_8
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4684-6750-5
Online ISBN: 978-1-4684-6748-2
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