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Exponential stability of impulsive stochastic functional differential equations. (English) Zbl 1222.60043

Authors’ abstract: “We investigate the \(p\)-th moment and almost sure exponential stability of impulsive stochastic differential equations with finite delay by using Lyapunov method. Several stability theorems of impulsive stochastic functional differential equations with finite delay are derived. These new results are employed to impulsive stochastic equations with bounded time-varying delays and stochastically perturbed equations. Also, an example and simulations are given to show that impulsive effects play an important role in \(p\)-th moment and almost sure exponential stability of stochastic functional differential equations with finite delay.”

MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
93E15 Stochastic stability in control theory
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