Abstract: By using the maximum likelihood estimation method, we considered the parameter estimation of a class of nonlinear stochastic differential equations driven by Lévy process. Firstly, the unbiasedness, the asymptotic consistency and the asymptotic normality of the estimator as T→∞ were discussed under time-continuous observations. Secondly, the continuous martingale part was approximated by a threshold method, and the unbiasedness and asymptotic normality of the estimator as n→∞ were obtained under the condition of high-frequency discrete observations and finite activity. Finally, the unbiasedness and asymptotic normality of estimator were verified by numerical simulation results.

Key words: nonlinear stochastic differential equation, maximum likelihood estimation (MLE), local Lipschitz, unbiasedness, asymptotic normality