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Fixed points and stability in neutral stochastic differential equations with variable delays. (English) Zbl 1255.60102
Summary: We consider the mean square asymptotic stability of a generalized linear neutral stochastic differential equation with variable delays by using the fixed point theory. An asymptotic mean square stability theorem with a necessary and sufficient condition is proved, which improves and generalizes some results due to Burton, Zhang and Luo. Two examples are also given to illustrate our results.
MSC:
60H10Stochastic ordinary differential equations
47H10Fixed point theorems for nonlinear operators on topological linear spaces
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