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Stability in mean of multi-dimensional uncertain differential equation

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  • Sheng, Yuhong
  • Shi, Gang

Abstract

A multi-dimensional uncertain differential equation is a type of differential equation. Stability of a multi-dimensional means insensitivity of the state of a system to small changes in the initial state. This paper presents a concept of stability in mean for multi-dimensional uncertain differential equation. Some stability theorems for the solution of multi-dimensional uncertain differential equation are given, in which some sufficient conditions for a multi-dimensional uncertain differential equation being stable in mean. In addition, this paper discusses their relationships between stability in measure and stability in mean.

Suggested Citation

  • Sheng, Yuhong & Shi, Gang, 2019. "Stability in mean of multi-dimensional uncertain differential equation," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 178-188.
    • Handle: RePEc:eee:apmaco:v:353:y:2019:i:c:p:178-188
    DOI: 10.1016/j.amc.2019.02.008
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    References listed on IDEAS

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    1. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
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    Cited by:

    1. Rong Gao, 2022. "Almost Sure Stability for Multi-Dimensional Uncertain Differential Equations," Mathematics, MDPI, vol. 10(19), pages 1-10, September.
    2. 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.
    3. Shen, Jiayu, 2020. "An uncertain sustainable supply chain network," Applied Mathematics and Computation, Elsevier, vol. 378(C).

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