The inverse uncertainty distribution of the solutions to a class of higher-order uncertain differential equations

Qiubao Wang; Zeman Wang; Zhong Liu; Zikun Han; Xiuying Guo

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arXiv · 2408.13571

The inverse uncertainty distribution of the solutions to a class of higher-order uncertain differential equations

Qiubao Wang·Zeman Wang·Zhong Liu·Zikun Han·Xiuying Guo

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Abstract

In this paper, we study the higher-order uncertain differential equations (UDEs) as defined by Kaixi Zhang (https://doi.org/10.1007/s10700-024-09422-0), mainly focus on the second-order case. We propose a pivotal condition (monotonicity in some sense, see more details in Section 3), introduce the concept of $\alpha$-paths of UDEs, and demonstrate its properties. Based on this, we derive the inverse uncertainty distribution of the solution.

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Qiubao Wang, Zeman Wang, Zhong Liu, Zikun Han, Xiuying Guo. 2024-08-24. The inverse uncertainty distribution of the solutions to a class of higher-order uncertain differential equations. https://arxiv.org/abs/2408.13571

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