Hitting time for correlated three-dimensional Brownian motion
Résumé
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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