[For the entire collection see Zbl 0728.00017.]
Authors apply the PDE vanishing viscosity techniques to the identification problem for a class of partially observed diffusion processes with small noise intensities. A parametric model for the stochastic processes with a small noise intensity and a corresponding model for the underlying deterministic processes are employed. The main result is that, if the deterministic model is identifiable, then the estimator similar to the maximum likelihood estimator (MLE) gives the true parameter value exactly. Also, the following consistency result is obtained. Any sequence of MLE converge in probability, as the intensity goes to zero, to the true parameter. A combination of Laplace’s asymptotic methods and PDE vanishing viscosity methods are used.