Moment estimation in uncertain differential equations based on the Milstein scheme

Han Tang and Xiangfeng Yang

Applied Mathematics and Computation, 2022, vol. 418, issue C

Abstract: Difference schemes are needed for approximating uncertain differential equations in applications. This paper mainly derives a new difference scheme called the Milstein scheme. It is theoretically shown that the Milstein scheme is superior to the previous Euler scheme. Then the Milstein scheme is applied to the method of moments so that the estimated uncertain differential equation fits the observations better. Moreover, the bias function is introduced to assess the precision of the estimation method. Finally, some numerical examples are given to verify the performance of both schemes and minimum cover estimation.

Keywords: Uncertainty theory; Uncertain differential equation; Method of moments; Milstein scheme (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:418:y:2022:i:c:s0096300321009085

DOI: 10.1016/j.amc.2021.126825

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