  Under some weak conditions, the first-passage time of the Brownian motion to
a continuous curved boundary is an almost surely finite stopping time. Its
probability density function (pdf) is explicitly known only in few particular
cases. Several mathematical studies proposed to approximate the pdf in a quite
general framework or even to simulate this hitting time using a discrete time
approximation of the Brownian motion. The authors study a new algorithm which
permits to simulate the first-passage time using an iterating procedure. The
convergence rate presented in this paper suggests that the method is very
efficient.
