Work

Initial Value Estimation of Uncertain Differential Equations Based on Residuals with Application in Financial Market

Year: 2025

Type: article

Abstract: The initial value estimation of uncertain differential equations refers to the process of estimating the initial state of a time-varying system using observed data when we cannot know exactly the initial state of the system in uncertain environments. In order to study the initial value estimation problem of uncertain differential equations, this paper constructs the confidence interval and point estimation of the initial value based on the residuals corresponding to the observed data. In order to further explain the initial value estimation based on residuals, this paper gives the confidence intervals and point estimations of the initial value for several specific uncertain differential equations, including linear, exponential, and mean-reversion uncertain differential equations. Finally, two numerical examples and an empirical study are also provided to illustrate the effectiveness of the proposed method.

Source: Axioms

DOI: 10.3390/axioms14020133

Authors: Waichon Lio, Yang Liu

Institution: Beihang University

Language: English

Topic: Fuzzy Systems and Optimization

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,896

Funders: National Natural Science Foundation of China, China Postdoctoral Science Foundation