Lévy过程驱使的非线性随机微分方程的参数估计  

Parameter Estimation of Nonlinear Stochastic Differential Equations Driven by Lévy Processes

作　　者：李明蔚 吕艳 LI Mingwei;L Yan(School of Mathematics and Statistics,Nanjing University of Science and Technology,Nanjing 210094,China)

机构地区：[1]南京理工大学数学与统计学院,南京210094

出　　处：《吉林大学学报（理学版）》2023年第3期531-539,共9页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11671204).

摘　　要：用极大似然估计方法,考虑一类由Lévy过程驱使的非线性随机微分方程参数估计问题.首先,在连续时间观测下讨论当T→∞时,估计量的无偏性、渐近一致性及其渐近正态性;其次,在高频离散观测且有限活跃条件下,利用阈值法逼近连续鞅部分,得到当n→∞时,估计量的无偏性和渐近正态性;最后,通过给出数值模拟结果验证估计量的无偏性和渐近正态性.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.

关 键 词：非线性随机微分方程 极大似然估计 局部Lipschitz 无偏性 渐近正态性 

分 类 号：O211.63[理学—概率论与数理统计]