On the statistical estimation of diffusion processes: a partial survey

Abstract

Data available on continuous-time diffusions are always sampled discretely in time. In most cases, the likelihood function of the observations is not directly computable. This survey covers a sample of the statistical methods that have been developed to solve this problem. We concentrate on some recent contributions to the literature based on three different approaches to the problem: an improvement of the Euler-Maruyama discretization scheme, the employment of Martingale Estimating Functions, and the application of Generalized Method of Moments (GMM).