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Hitting time for correlated three-dimensional Brownian motion

Abstract : Let X = (X1;X2;X3) be a three-dimensional correlated Brownian motion and T i be the first hitting time of a fixed level by Xi. The purpose of this paper is to compute the joint density of T = inf(T1, T2, T3) and X_T . We prove that the method of images used in dimension two by Iyengar leads us to a tiling three-dimensional space problem. A such a problem has only some particular solutions.
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Contributor : Diana Dorobantu <>
Submitted on : Tuesday, October 22, 2013 - 2:57:01 PM
Last modification on : Wednesday, July 8, 2020 - 12:43:14 PM
Long-term archiving on: : Thursday, January 23, 2014 - 4:26:15 AM


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  • HAL Id : hal-00846450, version 2


Christophette Blanchet-Scalliet, Areski Cousin, Diana Dorobantu. Hitting time for correlated three-dimensional Brownian motion. 2013. ⟨hal-00846450v2⟩



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