Instituto De Cibernetica Matematica Y Fisica an Approximate Innovation Method for the Estimation of Diffusion Processes from Discrete Data

In this paper an approximate innovation method is introduced for the estimation of diffusion processes given a set of discrete and noisy observations of some of their components. The method is based on a recent extension of Local Linearization filters to the general case of continuous-discrete state space models with multiplicative noise. This filtering method provides adequate approximations for the prediction and filter estimates that are required by the innovation method in the estimation of the unknown parameters and the unobserved component of the diffusion process. The performance of approximate innovation estimators is illustrated by means of numerical simulations.