Uncertain differential equation with jumps

Abstract

Uncertain differential equation is a type of differential equation driven by a canonical Liu process. Traditional uncertain differential equation can only deal with a continuous dynamic uncertain system. To model the sharp drifts embedded in an uncertain dynamic system, this paper proposes a type of uncertain differential equation driven by a canonical Liu process and an uncertain renewal process, which is called an uncertain differential equation with jumps. A sufficient condition for the proposed equation having a unique solution is first given, then a concept of stability for the proposed equation is provided in the sense of uncertain measure, and its sufficient condition is also derived.