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Existence, continuation, and uniqueness problems of stochastic impulsive systems with time delay. (English) Zbl 1205.60107
Summary: This paper studies stochastic impulsive systems with time delay, where the impulse times are state-dependent. Using Itô calculus, we develop the essential foundation of the theory of the mentioned system. In particular, we establish results on local and global existence, forward continuation, and uniqueness of adapted solutions.
MSC:
60H10Stochastic ordinary differential equations
34K20Stability theory of functional-differential equations
34K45Functional-differential equations with impulses
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