Affiliations: [a] College of Mathematics and System Science, Xinjiang University, Urumqi, China
| [b] LMAM, School of Mathematical Sciences and Center for Statistical Science, Peking University, Beijing, China
Correspondence:
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Corresponding author. Mingyao Ai, LMAM, School of Mathematical Sciences and Center for Statistical Science, Peking University, Beijing, China. E-mail: [email protected].
Abstract: This paper proposes three methods to estimate the parameters in uncertain differential equations (UDEs) based on discrete observation data. The first method is designed for a class of UDEs in which their solutions have the explicit expressions of uncertainty distribution. The second method is given to solve the estimation problem through the inverse uncertainty distribution. In the third method, the unknown parameters of UDEs are estimated by the solution of the corresponding α-path. These methods are interpreted to be efficient and practical by using a popular UDE with exponential solutions and obtaining the detailed estimators of the parameters.
