IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v343y2019icp49-56.html
   My bibliography  Save this article

Stability in distribution for uncertain delay differential equation

Author

Listed:
  • Jia, Lifen
  • Sheng, Yuhong

Abstract

As a type of differential equation, uncertain delay differential equation is driven by Liu process. Stability in measure, stability in mean and stability in moment for uncertain delay differential equation have been proposed. This paper mainly gives a concept of stability in distribution, and proves a sufficient condition for uncertain delay differential equation being stable in distribution as a supplement. Moreover, this paper further discusses their relationships among stability in distribution, stability in measure, stability in mean and stability in moment.

Suggested Citation

  • Jia, Lifen & Sheng, Yuhong, 2019. "Stability in distribution for uncertain delay differential equation," Applied Mathematics and Computation, Elsevier, vol. 343(C), pages 49-56.
    • Handle: RePEc:eee:apmaco:v:343:y:2019:i:c:p:49-56
    DOI: 10.1016/j.amc.2018.09.037
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300318308154
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2018.09.037?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Jia, Lifen & Lio, Waichon & Yang, Xiangfeng, 2018. "Numerical method for solving uncertain spring vibration equation," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 428-441.
    2. Yang, Xiangfeng, 2018. "Solving uncertain heat equation via numerical method," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 92-104.
    3. Xiangfeng Yang & Kai Yao, 2017. "Uncertain partial differential equation with application to heat conduction," Fuzzy Optimization and Decision Making, Springer, vol. 16(3), pages 379-403, September.
    4. Gao, Rong, 2017. "Uncertain wave equation with infinite half-boundary," Applied Mathematics and Computation, Elsevier, vol. 304(C), pages 28-40.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Gao, Yin & Gao, Jinwu & Yang, Xiangfeng, 2022. "The almost sure stability for uncertain delay differential equations based on normal lipschitz conditions," Applied Mathematics and Computation, Elsevier, vol. 420(C).
    2. Wang, Xiao & Ning, Yufu & Peng, Zhen, 2020. "Some results about uncertain differential equations with time-dependent delay," Applied Mathematics and Computation, Elsevier, vol. 366(C).
    3. Wang, Jian & Zhu, Yuanguo & Gu, Yajing & Lu, Ziqiang, 2021. "Solutions of linear uncertain fractional order neutral differential equations," Applied Mathematics and Computation, Elsevier, vol. 407(C).
    4. Caiwen Gao & Zhiqiang Zhang & Baoliang Liu, 2022. "Uncertain Population Model with Jumps," Mathematics, MDPI, vol. 10(13), pages 1-12, June.
    5. Gao, Yin & Gao, Jinwu & Yang, Xiangfeng, 2022. "Parameter estimation in uncertain delay differential equations via the method of moments," Applied Mathematics and Computation, Elsevier, vol. 431(C).
    6. Gao, Yin & Jia, Lifen, 2021. "Stability in mean for uncertain delay differential equations based on new Lipschitz conditions," Applied Mathematics and Computation, Elsevier, vol. 399(C).
    7. Jian Zhou & Yujiao Jiang & Athanasios A. Pantelous & Weiwen Dai, 2023. "A systematic review of uncertainty theory with the use of scientometrical method," Fuzzy Optimization and Decision Making, Springer, vol. 22(3), pages 463-518, September.
    8. Lu, Ziqiang & Zhu, Yuanguo, 2023. "Asymptotic stability in pth moment of uncertain dynamical systems with time-delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 212(C), pages 323-335.
    9. Shen, Jiayu, 2020. "An uncertain sustainable supply chain network," Applied Mathematics and Computation, Elsevier, vol. 378(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jian Zhou & Yujiao Jiang & Athanasios A. Pantelous & Weiwen Dai, 2023. "A systematic review of uncertainty theory with the use of scientometrical method," Fuzzy Optimization and Decision Making, Springer, vol. 22(3), pages 463-518, September.
    2. Yang, Xiangfeng & Ralescu, Dan A., 2021. "A Dufort–Frankel scheme for one-dimensional uncertain heat equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 181(C), pages 98-112.
    3. Jia, Lifen & Lio, Waichon & Yang, Xiangfeng, 2018. "Numerical method for solving uncertain spring vibration equation," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 428-441.
    4. Chen, Xin & Zhu, Yuanguo & Sheng, Linxue, 2021. "Optimal control for uncertain stochastic dynamic systems with jump and application to an advertising model," Applied Mathematics and Computation, Elsevier, vol. 407(C).
    5. Gao, Rong & Hua, Kexin, 2023. "A numerical method for solving uncertain wave equation," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    6. Lu Yang & Tingqing Ye & Haizhong Yang, 2022. "Uncertain seepage equation in fissured porous media," Fuzzy Optimization and Decision Making, Springer, vol. 21(3), pages 383-403, September.
    7. Abdulsalam, Athraa & Senu, Norazak & Majid, Zanariah Abdul & Long, Nik Mohd Asri Nik, 2024. "Development of high-order adaptive multi-step Runge–Kutta–Nyström method for solving special second-order ODEs," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 216(C), pages 104-125.
    8. Jia, Lifen & Liu, Xueyong, 2021. "Optimal harvesting strategy based on uncertain logistic population model," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    9. Yang, Xiangfeng & Liu, Yuhan & Park, Gyei-Kark, 2020. "Parameter estimation of uncertain differential equation with application to financial market," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    10. Pan, Zeyu & Gao, Yin & Yuan, Lin, 2021. "Bermudan options pricing formulas in uncertain financial markets," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    11. Liu, Z. & Yang, Y., 2021. "Selection of uncertain differential equations using cross validation," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    12. Zhang, Guidong & Sheng, Yuhong, 2022. "Estimating time-varying parameters in uncertain differential equations," Applied Mathematics and Computation, Elsevier, vol. 425(C).
    13. Gao, Rong & Ma, Nana & Sun, Gaoji, 2019. "Stability of solution for uncertain wave equation," Applied Mathematics and Computation, Elsevier, vol. 356(C), pages 469-478.
    14. Tang, Han & Yang, Xiangfeng, 2022. "Moment estimation in uncertain differential equations based on the Milstein scheme," Applied Mathematics and Computation, Elsevier, vol. 418(C).
    15. Shen, Jiayu, 2020. "An uncertain sustainable supply chain network," Applied Mathematics and Computation, Elsevier, vol. 378(C).
    16. Yang, Meng & Ni, Yaodong & Song, Qinyu, 2022. "Optimizing driver consistency in the vehicle routing problem under uncertain environment," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 164(C).
    17. Liu, Z., 2021. "Generalized moment estimation for uncertain differential equations," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    18. Liu, Z. & Yang, Y., 2021. "Pharmacokinetic model based on multifactor uncertain differential equation," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    19. Liu, Z. & Yang, Y., 2021. "Uncertain pharmacokinetic model based on uncertain differential equation," Applied Mathematics and Computation, Elsevier, vol. 404(C).
    20. Liu, Zhe & Li, Xiaoyang & Kang, Rui, 2022. "Uncertain differential equation based accelerated degradation modeling," Reliability Engineering and System Safety, Elsevier, vol. 225(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:343:y:2019:i:c:p:49-56. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.