Uncertain differential equation with jumps
Uncertain differential equation with jumps
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DOI：
10.1007/s00500-014-1392-8
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发表时间：
2014-07
期刊：
影响因子：
4.1
通讯作者：
K. Yao
中科院分区：
文献类型：
--
作者：
K. Yao
不确定微分方程是一类由正则刘过程驱动的微分方程。传统的不确定微分方程只能处理连续动态的不确定系统。为了模拟不确定动态系统中的急剧漂移，本文提出了一种由正则刘过程和不确定更新过程驱动的不确定微分方程，称为带跳跃的不确定微分方程。首先给出了所提方程具有唯一解的充分条件，然后给出了所提方程在不确定测度意义上的稳定性概念，并推导了其充分条件。
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.