Estimating Parameters of Diffusion Process with Unreachable Boundary

In the present paper we consider methods of estimating unknown parameters in diffusion-type models for continuous and discrete observations. It is assumed that the estimated parameters enter the model linearly. For continuously observed processes the maximum likelihood method is used. For diffusion processes, which are observed discretely and are described by stochastic differential equations, martingale methods of parameter estimations are developed based on the likelihood function approximation. Consistent and asymptotically normal parameter estimates are obtained. © 2015, Springer Science+Business Media New York.