Least Squares Estimation in Uncertain Differential Equations

Abstract

Uncertain differential equations are a type of differential equations driven by Liu processes. How to estimate the parameters in an uncertain differential equation based on the observed data is a crucial problem in the real applications of these equations. By means of the least squares estimation, this article proposes a principle of minimum noise as an approach to the problem. Following this principle, the estimates of the parameters in some special types of uncertain differential equations are derived, which are represented as functions of the observed data. In addition, some numerical experiments are performed to illustrate the principle.