{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,4]],"date-time":"2026-07-04T01:52:01Z","timestamp":1783129921315,"version":"3.54.6"},"reference-count":40,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2024,10,15]],"date-time":"2024-10-15T00:00:00Z","timestamp":1728950400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["11901145"],"award-info":[{"award-number":["11901145"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>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\u2013Uhlenbeck process in probability, named the uncertain threshold Ornstein\u2013Uhlenbeck 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\u2013Uhlenbeck process mentioned in this paper. The paper concludes with brief remarks and possible future directions.<\/jats:p>","DOI":"10.3390\/sym16101372","type":"journal-article","created":{"date-parts":[[2024,10,18]],"date-time":"2024-10-18T05:50:05Z","timestamp":1729230605000},"page":"1372","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Parameter Estimation of Uncertain Differential Equations Driven by Threshold Ornstein\u2013Uhlenbeck Process with Application to U.S. Treasury Rate Analysis"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8259-9990","authenticated-orcid":false,"given":"Anshui","family":"Li","sequence":"first","affiliation":[{"name":"School of Mathematics, Physics and Information, Shaoxing University, Shaoxing 312000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiajia","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mathematics, Physics and Information, Shaoxing University, Shaoxing 312000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lianlian","family":"Zhou","sequence":"additional","affiliation":[{"name":"School of Mathematics, Physics and Information, Shaoxing University, Shaoxing 312000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,10,15]]},"reference":[{"key":"ref_1","first-page":"519","article-title":"Stochastic integral","volume":"20","year":"1944","journal-title":"Proc. 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