Stability in p-th moment for uncertain differential equation with jumps

Article type: Research Article

Authors: Ma, Weimin^a | Liu, Liying^{a; b; *} | Zhang, Xingfang^b

Affiliations: [a] School of Economics and Management, Tongji University, Shanghai, China | [b] School of Mathematics Science, Liaocheng University, Liaocheng, China

Correspondence: [*] Corresponding author. Liying Liu. Tel.: +86 013869538293; Fax: +86 0635 8539846; E-mails: [email protected]; [email protected].

Abstract: Uncertain differential equation with jumps is a type of differential equations driven by both Liu process and the uncertain renewal process. Stability of uncertain differential equation with jumps, playing an important role in uncertain differential equation with jumps, means insensitivity of the state of a system with a small changes in the initial state. This paper focuses on the stability in p-th moment for uncertain differential equation with jumps, including the concept of stability in p-th moment, and the sufficient condition for uncertain differential equation with jumps being stable in p-th moment. In addition, the relationship between stability in measure and stability in p-th moment for the uncertain differential equation with jumps is also discussed.

Keywords: Uncertainty theory, uncertain differential equation, stability, uncertain process

DOI: 10.3233/JIFS-17332

Journal: Journal of Intelligent & Fuzzy Systems, vol. 33, no. 3, pp. 1375-1384, 2017