An Efficient Algorithm to Simulate a Brownian Motion Over Irregular Domains (Communications in Computational Physics, 2010)
In this paper, we present an algorithm to simulate a Brownian motion bycoupling two numerical schemes: the Euler scheme with the random walk on thehyper-rectangles. This coupling algorithm has the advantage to be able to computethe exit time and the exit position of a Brownian motion from an irregular boundeddomain (with corners at the boundary), and being of order one with respect to thetime step of the Euler scheme. The efficiency of the algorithm is studied through somenumerical examples by comparing the analytical solution with the Monte Carlo solutionof some Poisson problems. The Monte Carlo solution of these PDEs requiressimulating Brownian motions of different types (natural, reflected or drifted) over anirregular domain.