Yang Liu

Uncertain delay differential equations can simultaneously describe uncertain disturbances and time-delay effects during the evolution process of a system, and parameter estimation is a crucial step in the application of uncertain delay differential equations. To address the issue of equal-weight imbalance in residual-based moment estimation, this paper investigates a weighted moment estimation method for uncertain delay differential equations based on uncertain theory. Specifically, a counterexample is presented to illustrate the equal-weight imbalance problem in the existing residual-based moment estimation, and a weighted moment estimation approach for uncertain delay differential equations is derived based on the idea of relative deviation. Subsequently, a numerical algorithm for calculating the weighted moment estimation is designed, and an empirical study modeling population birth rates is also provided to demonstrate the effectiveness of the method and numerical algorithm proposed in this paper.

1. Uncertain differential equation (UDE), as is well known, was a class of differential equation under the action of uncertain processes. Since UDE was first proposed by Liu (2008) to cope with unc...

Multifactor uncertain differential equations (MUDEs) are effective tools to model dynamic systems under multi-source noise. With the widespread use of MUDEs, parameter estimation as the bridge between the observed data and the MUDE becomes increasingly important. Thus, how to estimate unknown parameters in a MUDE under a multi-source noise environment is a challenge. To address this, this paper innovatively proposes a moment method to estimate the unknown parameters in a MUDE and illustrates two numerical examples to show the process of estimating parameters. Furthermore, since the system or environment is complex and constantly changing, the parameters in the MUDE are not constants but time-varying functions in many cases. Therefore, parameter estimation for time-varying functions is another challenge. In order to deal with this, this paper develops a method of parameter estimation for time-varying functions in the MUDE based on the moment method. As an application, this method of parameter estimation for time-varying functions is used to model China Merchants Bank stock.