不确定微分方程中时变参数的极大似然估计

张贵东; 盛玉红

doi:10.13568/j.cnki.651094.651316.2021.09.22.0002

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不确定微分方程中时变参数的极大似然估计

数理科学 | 更新时间：2026-01-21

- 不确定微分方程中时变参数的极大似然估计
- 不确定微分方程中时变参数的极大似然估计
- 新疆大学学报（自然科学版中英文） 2022年39卷第4期页码：421-431
- 作者机构：
  
  新疆大学数学与系统科学学院
- 作者简介：
- 基金信息：
  
  国家自然科学基金（12061072）;国家重点研发计划项目（2018YFC0825504）
- DOI：10.13568/j.cnki.651094.651316.2021.09.22.0002
  中图分类号： O212.1
- 纸质出版：2022
- 稿件说明：
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[1]张贵东,盛玉红.不确定微分方程中时变参数的极大似然估计[J].新疆大学学报(自然科学版)(中英文),2022,39(04):421-431.
[1]张贵东,盛玉红.不确定微分方程中时变参数的极大似然估计[J].新疆大学学报(自然科学版)(中英文),2022,39(04):421-431. DOI： 10.13568/j.cnki.651094.651316.2021.09.22.0002.

DOI：10.13568/j.cnki.651094.651316.2021.09.22.0002.

摘要

对不确定微分方程中的时变参数进行估计．首先利用不确定极大似然估计的方法获得与观测值时刻对应的时变参数估计值，然后将这一系列时变参数估计值利用回归分析的方法进行线性或者非线性拟合，得到时变参数估计．其次为了验证时变参数估计值的合理性，给出了带有时变参数的不确定微分方程的α-轨道及其性质和可决系数R2，对时变参数是否合理进行了评判．最后给出一个新型冠状病毒传播模型的数值实例验证估计方法的有效性．

Abstract

This paper focuses on the estimation of time-varying parameters in uncertain differential equations.Firstly

the time-varying parameter estimates corresponding to the moments of observations were obtained by using the method of uncertain maximum likelihood estimation

and then this series of time-varying parameter estimates were fitted linearly or non-linearly by using the method of regression analysis to obtain the time-varying parameter estimates. Secondly

in order to evaluate the reasonableness of the time-varying parameter estimates

the α-paths and properties of the uncertain differential equations with time-varying parameters and the decidability factor R2were given

and the reasonableness of the time-varying parameters was evaluated. Finally

the validity of the approach was tested by using the example of the COVID-19 infectious disease model.

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