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Stability in mean for uncertain differential equation with jumps

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  • Gao, Rong

Abstract

An uncertain differential equation with jumps is a type of uncertain differential equation driven by Liu process and uncertain renewal process, which is used to model discontinuous systems. Up to now, the stability in measure and almost sure stability for such an equation have been studied. The above two types of stability cannot be applied to all cases, so this paper aims at presenting a concept of stability in mean for an uncertain differential equation with jumps as a supplement. Most important of all, a stability theorem is given for an uncertain differential equation with jumps being stable in mean. And some examples are proposed to show how to use the theorem to judge whether the uncertain differential equation with jumps is stable in mean.

Suggested Citation

  • Gao, Rong, 2019. "Stability in mean for uncertain differential equation with jumps," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 15-22.
    • Handle: RePEc:eee:apmaco:v:346:y:2019:i:c:p:15-22
    DOI: 10.1016/j.amc.2018.09.068
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    References listed on IDEAS

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    1. Gao, Rong, 2016. "Milne method for solving uncertain differential equations," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 774-785.
    2. Rong Gao & Yan Sun & Dan A. Ralescu, 2017. "Order statistics of uncertain random variables with application to k-out-of-n system," Fuzzy Optimization and Decision Making, Springer, vol. 16(2), pages 159-181, June.
    3. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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    Cited by:

    1. Caiwen Gao & Zhiqiang Zhang & Baoliang Liu, 2022. "Uncertain Population Model with Jumps," Mathematics, MDPI, vol. 10(13), pages 1-12, June.
    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. Song, Bo & Zhang, Ya & Park, Ju H., 2021. "H∞ control for Poisson-driven stochastic systems," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    4. Shen, Jiayu, 2020. "An uncertain sustainable supply chain network," Applied Mathematics and Computation, Elsevier, vol. 378(C).

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