Parameter Estimation for A Class of Diffusion Pro cess from Discrete Observation

  • Chao Wei
  • Fang Xu
Keywords: Diffusion process, parameter estimation, discrete observation, consistency, asymptotic normality


This pap er is concerned with the parameter es tim ation problem for a class of diffusion pro cess from discrete observations. The approximate likeliho o d function is given by us ing a Riemann sum and an Itˆo sum to approximate the inte grals in the continuous-time likeliho o d function. The consistency of the maximum likeliho od 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 ergo dic theorem. The results are applied to the hyp erb olic process.