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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.13571 |
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| _version_ | 1866909294791753728 |
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| author | Wang, Qiubao Wang, Zeman Liu, Zhong Han, Zikun Guo, Xiuying |
| author_facet | Wang, Qiubao Wang, Zeman Liu, Zhong Han, Zikun Guo, Xiuying |
| contents | 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 $α$-paths of UDEs, and demonstrate its properties. Based on this, we derive the inverse uncertainty distribution of the solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_13571 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The inverse uncertainty distribution of the solutions to a class of higher-order uncertain differential equations Wang, Qiubao Wang, Zeman Liu, Zhong Han, Zikun Guo, Xiuying Probability 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 $α$-paths of UDEs, and demonstrate its properties. Based on this, we derive the inverse uncertainty distribution of the solution. |
| title | The inverse uncertainty distribution of the solutions to a class of higher-order uncertain differential equations |
| topic | Probability |
| url | https://arxiv.org/abs/2408.13571 |