一类带有小的对称α稳定噪声的随机微分方程的参数估计  

Parameter Estimation for a Family of Stochastic Differential Equations with Small Symmetricα-stable Noises

作　　者：潘玉荣[1] 刘晓雁 PAN Yu-rong;LIU Xiao-yan(School of Science,Bengbu University,Bengbu,233030,Anhui;College of Arts and Sciences,University of La Verne,La Verne,91750,California,USA)

机构地区：[1]蚌埠学院理学院,安徽蚌埠233030 [2]拉文大学文理学院,美国加州拉文91750

出　　处：《蚌埠学院学报》2020年第2期78-82,共5页Journal of Bengbu University

基　　金：安徽省高校自然科学基金重点项目(KJ2017A568);安徽省自然科学基金(1808085MA02);安徽省质量工程项目(2019jyxm0476);蚌埠学院教研项目(2018JYXML8)。

摘　　要：考虑一类带有小的对称α稳定噪声的随机微分方程的参数估计问题,基于离散观测数据,建立了漂移项未知参数的条件最小二乘估计量,并详细给出了当ε→0且n→∞时,该估计量相合性和渐近分布的证明。The parameter estimation problem for a family of Stochastic Differential Equations with small symmetric α-stable noises was considered in this paper.Based on discrete observations,the conditional least squares estimator of the unknown drift parameter was established,and the proof of the consistency and the asymptotic distributions of our estimators is given as ε→0 and n→∞ simultaneously.

关 键 词：α稳定过程 参数估计 相合性 渐近分布 

分 类 号：O211.63[理学—概率论与数理统计]