Parameter estimation in uncertain differential equations based on the solution
The parameter estimation of uncertain differential equation is a significant subject in uncertainty theory. This paper introduces three methods for uncertain differential equations to estimate parameters. These three methods are based on different forms of solutions, and they are the solution of the...
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| Published in | Mathematical methods in the applied sciences Vol. 44; no. 11; pp. 9441 - 9452 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Freiburg
Wiley Subscription Services, Inc
30.07.2021
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0170-4214 1099-1476 |
| DOI | 10.1002/mma.7370 |
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| Abstract | The parameter estimation of uncertain differential equation is a significant subject in uncertainty theory. This paper introduces three methods for uncertain differential equations to estimate parameters. These three methods are based on different forms of solutions, and they are the solution of the linear uncertain differential equation, the solution of uncertain differential equation with the Euler scheme, and the solution of uncertain differential equation with the midpoint scheme. According to the correlation operation of the solution obeying the same distribution as that of the observed value, the unknown parameters can be obtained. Several numerical examples are used to illustrate the proposed parameter estimation methods. |
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| AbstractList | The parameter estimation of uncertain differential equation is a significant subject in uncertainty theory. This paper introduces three methods for uncertain differential equations to estimate parameters. These three methods are based on different forms of solutions, and they are the solution of the linear uncertain differential equation, the solution of uncertain differential equation with the Euler scheme, and the solution of uncertain differential equation with the midpoint scheme. According to the correlation operation of the solution obeying the same distribution as that of the observed value, the unknown parameters can be obtained. Several numerical examples are used to illustrate the proposed parameter estimation methods. |
| Author | Sheng, Yuhong Zhang, Nan |
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| Cites_doi | 10.1007/s10700-014-9204-2 10.1007/978-3-540-73165-8_5 10.1007/s10700-012-9139-4 10.3233/IFS-130812 10.3233/IFS-120688 10.1016/j.asej.2014.10.021 10.1007/s00500-020-04951-3 10.3233/JIFS-162080 10.1016/j.amc.2016.11.012 10.1155/2014/369029 10.1007/s10700-019-09310-y 10.1109/TAC.1968.1099025 10.1016/0047-259X(75)90038-X 10.1109/TFUZZ.2019.2939984 10.1007/s10700-010-9073-2 10.1142/S0218488513400060 |
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| Title | Parameter estimation in uncertain differential equations based on the solution |
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