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Moment estimation for parameters in high-order uncertain differential equations

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  • Liu, Zhe
  • Yang, Ying

Abstract

As a type of differential equations with high-order derivatives of uncertain processes, high-order uncertain differential equations are widely applied to modelling dynamic systems in uncertain environment, which usually involve unknown parameters to be estimated. Since observations are always discrete in practice, based on these discrete observations of solution processes, we propose moment estimations for unknown parameters by Euler method approximation of high-order uncertain differential equations. Matching sample moments with corresponding population moments, a system of equations whose solution is the moment estimation of the set of unknown parameters is derived. Finally, some examples illustrate our method in detail.

Suggested Citation

  • Liu, Zhe & Yang, Ying, 2022. "Moment estimation for parameters in high-order uncertain differential equations," Applied Mathematics and Computation, Elsevier, vol. 433(C).
    • Handle: RePEc:eee:apmaco:v:433:y:2022:i:c:s0096300322004738
    DOI: 10.1016/j.amc.2022.127399
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    References listed on IDEAS

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    6. Liu, Z., 2021. "Generalized moment estimation for uncertain differential equations," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    7. Liu, Z. & Yang, Y., 2021. "Selection of uncertain differential equations using cross validation," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
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