关键词: 渐近正态性, 非线性随机微分方程, 无偏性, 参数估计

Abstract: By using the maximum likelihood estimation (MLE) method , we considered the parameter estimation problem of a class of nonlinear stochas tic differential equations with small perturbation. We discussed the properties of the esitmator as the small perturbation parameter ε→0 or ti me T→∞, and proved that the estimator of unknown parameter had unbiasedness and asymptotic consistency as ε→0. When ε took a fix ed value and ε→0, we gave the asymptotic distribut ion of the estimator α^^ε as T→∞ respectively. Finallay, we gave the numerical simulation results to veri fy the unbiasedness and asymptotic normality of estimator.

Key words: parameter estimation, asymptotic normality, unbiasedness, nonlinear stochastic differential equation