A NEW LARGE DEVIATIONS PRINCIPLE IN NONLINEAR FILTERING THEORY

Consider the couple "signal-observation" (X(t), epsilon Y(t)epsilon) is-an-element-of R(n) x R(l), solution of [GRAPHICS] where epsilon > 0, sigma-1,...,sigma-r, sigma-1 approximately, sigma-l approximately and b are regular vector fields on R(n). h is a regular map from R(n) to R(l), B = (B1,...,B(r), B approximately = (B1 approximately,...,B(l) approximately) are two independent brownian motions. When epsilon down 0 and x-epsilon --> x, we prove, under some conditions, a large deviations principle for the conditional probability distribution M-epsilon (.,d-omega) of the "signal" process X-epsilon = (X(t)epsilon)t is an-element-of [0, T] given the "observation" Y-epsilon = (Y(t)epsilon)t is-an-element-of [0, T].