Stability in mean for uncertain differential equation with jumps.

*(English)*Zbl 1428.60076Summary: An uncertain differential equation with jumps is a type of uncertain differential equation driven by Liu process and uncertain renewal process, which is used to model discontinuous systems. Up to now, the stability in measure and almost sure stability for such an equation have been studied. The above two types of stability cannot be applied to all cases, so this paper aims at presenting a concept of stability in mean for an uncertain differential equation with jumps as a supplement. Most important of all, a stability theorem is given for an uncertain differential equation with jumps being stable in mean. And some examples are proposed to show how to use the theorem to judge whether the uncertain differential equation with jumps is stable in mean.

##### MSC:

60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |

28E10 | Fuzzy measure theory |

34D20 | Stability of solutions to ordinary differential equations |

34F05 | Ordinary differential equations and systems with randomness |

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