Stability Analysis for a Class of Stochastic Differential Equations with Impulses
Mingli Xia, Linna Liu, Jianyin Fang, Yicheng Zhang
Abstract
This paper is concerned with the problem of asymptotic stability for a class of stochastic differential equations with impulsive effects. A sufficient criterion on asymptotic stability is derived for such impulsive stochastic differential equations via Lyapunov stability theory, bounded difference condition and martingale convergence theorem. The results show that the impulses can facilitate the stability of the stochastic differential equations when the original system is not stable. Finally, the feasibility of our results is confirmed by two numerical examples and their simulations.
Topics & Concepts
MathematicsExponential stabilityStochastic differential equationMartingale (probability theory)Comparison theoremStochastic partial differential equationLyapunov functionStability (learning theory)Applied mathematicsDifferential equationMathematical analysisBounded functionClass (philosophy)Nonlinear systemComputer sciencePhysicsQuantum mechanicsMachine learningArtificial intelligenceStability and Controllability of Differential EquationsNonlinear Differential Equations AnalysisMathematical and Theoretical Epidemiology and Ecology Models