中文摘要：

在小噪声扰动条件下研究二维扩散的极大似然估计问题,构建极大似然函数,得到了极大似然估计,并证明了参数估计的无偏性、强相合性和渐近正态性。此外,研究了小参数δ趋于0时,原始方程的参数估计概率收敛到极限方程的参数估计,数值模拟证明了理论结果。

英文摘要：

The paper deals with the maximum likelihood estimation of two dimension diffusion with small noise perturbations and establishes maximum likelihood function. It does not work out the maximum likelihood estimation,but also proves the unbiased property,strong consistency,and asymptotic normality of the parameter estimation. The innovation point of this paper is the finding that the parameter estimator of the former equation convergence in probability the estimator of the limit equation when parameter is close to zero. Simulation results demonstrate our theoretical finding.