一类离散观测下非线性随机系统估计量的局部渐近正态性  

Local Asymptotic Normality of a Class of Nonlinear Stochastic Systems with Unknown Perturbation Parameter in Discretely Observed

作　　者：阚秀 舒慧生[3] KAN Xiu;SHU Huisheng(School of Mathematics,Southeast University,Nanjing 210096,China;School of Electronic and Electrical Engineering,Shanghai University of Engineering Science,Shanghai 201620,China;College of Science,Donghua University,Shanghai 201620,China)

机构地区：[1]东南大学数学学院,江苏南京210096 [2]上海工程技术大学电子电气工程学院,上海201620 [3]东华大学理学院,上海201620

出　　处：《东华大学学报（自然科学版）》2020年第1期168-174,共7页Journal of Donghua University(Natural Science)

基　　金：国家自然科学基金资助项目(61673103,61403248);上海市青年科技英才扬帆计划资助项目(14YF1409800)。

摘　　要：研究了一类离散观测下含未知参数的非线性随机系统的渐近性问题,对似然率函数和极大似然估计量的近似值分别进行精确度分析,建立了似然率随机域来分析似然率的渐近动态特征,并借助积分中心极限定理等数学工具分析得到似然率随机域满足局部渐近正态性的充分条件,并进一步给出Berstein-Von-Mises型有界定理。The asymptotic properties were investigated for a class of discretely time observed nonlinear stochastic system with unknown perturbation parameter.The accuracies of the likelihood function and the approximate maximum likelihood estimator were analyzed.The likelihood ratio random field was established to analyse the asymptotic behavior of the approximate maximum likelihood estimator.By central limit theorem and stochastic analysis approaches,sufficient conditions were established to ensure the approximate maximum likelihood estimator satisfied local asymptotic normality.Moreover,a version of Bernstein-Von-Mises type theory was proposed in the end.

关 键 词：局部渐近正态性 弱收敛性 离散时间观测 非线性随机系统 

分 类 号：O212.1[理学—概率论与数理统计]