Stability analysis of backward uncertain differential equations

ABSTRACT

Backward uncertain differential equation is a class of uncertain differential equations with a terminal value. This paper focuses on its stability analysis. At first, this paper gives the concepts of stability in measure, stability in mean and stability in pth moment for backward uncertain differential equations. In addition, some sufficient conditions in the form of theorem for backward uncertain differential equations being stable in measure, in mean and in pth moment are derived. Meanwhile, this paper further discusses the relationship between these three types of stability.

KEYWORDS:

• Uncertainty theory
• backward uncertain differential equation
• stability in measure
• stability in mean
• stability in pth moment

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Xiao Wang  http://orcid.org/0000-0002-0663-6865

Additional information

Funding

This work was supported by National Natural Science Foundation of China [grant number 11701338], China Postdoctoral Science Foundation [grant number 2019M650551] and Natural Science Foundation of Shandong Province [grant number ZR2016AP12].