Affiliations: [a] College of Mathematical and System Sciences, Xinjiang University, Urumqi, China
| [b] School of Information Science and Engineering, Xinjiang University, Urumqi, China
| [c] Department of Computer Science and Technology, Tsinghua University, Beijing, China
Correspondence:
[*]
Corresponding author. Gang Shi, School of Information Science and Engineering, Xinjiang University, Urumqi 830046, China. Tel: +86 13579998016; E-mail: [email protected].
Abstract: Multifactor uncertain differential equation is a type of differential equation driven by the multiple Liu processes. Stability of a multifactor uncertain differential equation plays a very important role in differential equation which means insensitivity of the state of a system to small changes in the initial state. This paper presents a concept of the p-th moment stability of multifactor uncertain differential equation. Some stability theorems for the solution of multifactor uncertain differential equation are given, in which some sufficient conditions for a multifactor uncertain differential equation being stable in p-th moment and a sufficient and necessary condition for a linear multifactor uncertain differential equation being stable in p-th moment are provided. In addition, this paper discusses the relationships among stability in p-th moment, stability in measure and stability in mean.
Keywords: Uncertainty theory, multifactor uncertain differential equation, moment stability
