The model consists of a signal process X which is a general Brownian diffusion process and an observation process Y , also a diffusion process, which is supposed to be correlated to the signal process. We suppose that the process Y is observed from time 0 to s > 0 at discrete times and aim to estimate, conditionally on these observations, the probability that the non-observed process X crosses a fixed barrier after a given time t > s. We formulate this problem as a usual nonlinear filtering problem and use optimal quantization and Monte Carlo simulations techniques to estimate the involved quantities. |