In this paper a finite-dimensional diffusion is observed in the presence of an additive Brownian motion. A large deviations result is obtained for the conditional probability distribution of the diffusion given the observations as the noise variances go to zero.
"Asymptotic Bayesian Estimation of a First Order Equation with Small Diffusion." Ann. Probab. 12 (3) 890 - 902, August, 1984. https://doi.org/10.1214/aop/1176993238