文献类型：期刊文献

英文题名：Parameter Estimation of Uncertain Differential Equations Driven by Threshold Ornstein-Uhlenbeck Process with Application to US Treasury Rate Analysis

作者：Li, Anshui[1];Wang, Jiajia[1];Zhou, Lianlian[1]

机构：[1]Shaoxing Univ, Sch Math Phys & Informat, Shaoxing 312000, Peoples R China

年份：2024

卷号：16

期号：10

外文期刊名：SYMMETRY-BASEL

收录：SCI-EXPANDED(收录号：WOS:001342923600001)、、Scopus(收录号：2-s2.0-85207684954)、WOS

基金：Anshui Li's work is supported by the National Natural Science Foundation of China (No. 11901145).

语种：英文

外文关键词：uncertainty theory; uncertain differential equation; uncertain threshold Ornstein-Uhlenbeck process; maximum likelihood estimation; moment method; residual analysis

外文摘要：Uncertain differential equations, as an alternative to stochastic differential equations, have proved to be extremely powerful across various fields, especially in finance theory. The issue of parameter estimation for uncertain differential equations is the key step in mathematical modeling and simulation, which is very difficult, especially when the corresponding terms are driven by some complicated uncertain processes. In this paper, we propose the uncertainty counterpart of the threshold Ornstein-Uhlenbeck process in probability, named the uncertain threshold Ornstein-Uhlenbeck process, filling the gaps of the corresponding research in uncertainty theory. We then explore the parameter estimation problem under different scenarios, including cases where certain parameters are known in advance while others remain unknown. Numerical examples are provided to illustrate our method proposed. We also apply the method to study the term structure of the U.S. Treasury rates over a specific period, which can be modeled by the uncertain threshold Ornstein-Uhlenbeck process mentioned in this paper. The paper concludes with brief remarks and possible future directions.