  We provide a new methodology to simulate the first exit times of a vector of
Brownian motions from an orthant. This new approach can be used to simulate the
first exit times of dimension higher than two. When at least one Brownian
motion has non-zero drift, the joint density function of the first exit times
in N dimensions needs to be known, or approximated. However, when the drifts
are all zero, a simpler simulation algorithm is obtained without using the
joint density function.
