Parameter estimation in uncertain differential equations based on the solution

• Published in: Mathematical methods in the applied sciences Vol. 44; no. 11; pp. 9441 - 9452
• Main Authors: Sheng, Yuhong, Zhang, Nan
• Format: Journal Article
• Language: English
• Published: Freiburg Wiley Subscription Services, Inc 30.07.2021
• Subjects: Differential equations; Parameter estimation; Parameter uncertainty; uncertain differential equation; uncertainty theory
• ISSN: 0170-4214; 1099-1476
• DOI: 10.1002/mma.7370

The parameter estimation of uncertain differential equation is a significant subject in uncertainty theory. This paper introduces three methods for uncertain differential equations to estimate parameters. These three methods are based on different forms of solutions, and they are the solution of the linear uncertain differential equation, the solution of uncertain differential equation with the Euler scheme, and the solution of uncertain differential equation with the midpoint scheme. According to the correlation operation of the solution obeying the same distribution as that of the observed value, the unknown parameters can be obtained. Several numerical examples are used to illustrate the proposed parameter estimation methods.