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Asymptotic mixed normality of approximate maximum likelihood estimator of drift parameters in ergodic diffusion model

We assume that the ergodic diffusion X satisfies a stochastic differential equation of the form: dXt=μ(Xt, θ)dt+σ0ν(Xt)dWt, with unknown drift parameter θ and known diffusion coefficient parameter σ0. We prove that the difference between approximate maximum likelihood estimator of drift parameter obtained from discrete observations along time interval, and MLE obtained from continuous observations along time interval has asymptotic mixed normal distribution with covariance matrix which depends on true parameter value and on path (Xt, t≥0) when n and T goes to infinity.

asymptotic mixed normality, ergodic diffusion, discrete observation, parameter estimation

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