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April, 1992 Brownian Exit Distributions from Normal Balls in $S^3 \times H^3$
H. R. Hughes
Ann. Probab. 20(2): 655-659 (April, 1992). DOI: 10.1214/aop/1176989797


Let $X_t$ be Brownian motion on a Riemannian manifold $M$ started at $m$ and let $T$ be the first time $X_t$ exits a normal ball about $m$. The first exit time $T$ for $M = S^3 \times H^3$ has the same distribution as the first exit time for $M = \mathbf{R}^6$. For $M = S^3 \times H^3, T$ and $X_T$ are independent random variables.


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H. R. Hughes. "Brownian Exit Distributions from Normal Balls in $S^3 \times H^3$." Ann. Probab. 20 (2) 655 - 659, April, 1992.


Published: April, 1992
First available in Project Euclid: 19 April 2007

zbMATH: 0761.58054
MathSciNet: MR1159565
Digital Object Identifier: 10.1214/aop/1176989797

Primary: 58G32
Secondary: 53B20 , 60J65

Keywords: Brownian motion , diffusions on manifolds , exit time and place , transformation of drift

Rights: Copyright © 1992 Institute of Mathematical Statistics

Vol.20 • No. 2 • April, 1992
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