Estimation for diffusion processes from discrete observation

The maximum likelihood estimation of the unknown parameter of a diffusion process based on an approximate likelihood given by the discrete observation is treated when the diffusion coefficients are unknown and the condition for "rapidly increasing experimental design" is broken. The asymptotic normality of the joint distribution of the maximum likelihood estimator of the unknown parameter in the drift term and an estimator of the diffusion coefficient matrix is proved. We prove the weak convergence of the likelihood ratio random field, which serves to show the asymptotic behavior of the likelihood ratio tests with restrictions.