Affiliations: [a] School of Information Science and Engineering, Xinjiang University, Urumqi, China
| [b] College of Mathematical and System Sciences, Xinjiang University, Urumqi, China
Correspondence:
[*]
Corresponding author. Yuhong Sheng, College of Mathematical and System Sciences, Xinjiang University, Urumqi 830046, China. Tel.: +86 18167978160; E-mail: sheng-yh12@mails.tsinghua.edu.cn.
Abstract: Backward uncertain differential equation is a specical type of differential equation driven by a Liu process. There are some concepts of stability such as stability in measure, stability in mean, stability in p-th moment, stability moment exponential and almost sure stability of backward uncertain differential equations have been proposed. As a supplement, this paper gives a concept of stability in uncertain distribution of backward uncertain differential equation. Some sufficient conditions for a backward uncertain differential equation being stable in uncertain distribution are provided. In addition, this paper further discusses their relationships among stability in uncertain distribution, stability in uncertain measure, stability in mean and stability in p-th moment. Last, this paper discusses some examples to illustrate the theoretical considerations.
Keywords: Uncertain distribution, uncertain process, backward uncertain differential equation, stability in distribution
