Parameter estimation in uncertain differential equations based on the solution

Abstract

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.