Abstract
This paper is concerned with the parameter estimation problem for a class of diffusion process from discrete observations. The approximate likelihood function is given by using a Riemann sum and an Itˆo sum to approximate the integrals in the continuous-time likelihood function. The consistency of the maximum likelihood estimator and the asymptotic normality of the error of estimation are proved by applying the martingale moment inequality, Holder’s inequality, Chebyshev inequality, B-D-G inequality and uniform ergodic theorem. The results are applied to the hyperbolic process.
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