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Robustness of general decay stability of nonlinear neutral stochastic functional differential equations with infinite delay. (English) Zbl 1223.93096

Summary: This paper establishes the existence-and-uniqueness theorem of neutral stochastic functional differential equations with infinite delay and examines the almost sure stability of this solution with general decay rate. This result may be used to examine almost sure robust stability. To illustrate our idea more carefully, we discuss a scalar stochastic integro-differential equation of neutral type and its asymptotic stability, including the exponential stability and the polynomial stability.

MSC:

93D09 Robust stability
93E03 Stochastic systems in control theory (general)
34K40 Neutral functional-differential equations
93C10 Nonlinear systems in control theory
34K50 Stochastic functional-differential equations
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