Simulation of a diffusion process by using the importance sampling paradigm

We construct in this paper a Monte Carlo method in order to approach solutions of multi-dimensional Stochastic Differential Equations processes which relies on the importance sampling technique. Our method is based on the random walk on squares/rectangles method and the main interest of this construction is that the weights are easily computed from the density of the one-dimensional Brownian motion. The advantage we take on the Euler scheme is that this method allows us to get a better simulation of diffusions when one has really to take care of the boundary conditions. Moreover, it provides a good alternative to perform variance reduction techniques and simulation of rare events.

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