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In this paper, the problem of asymptotic stability for stochastic Hopfield neural networks (HNNs) with time delays is investigated. New delay-dependent stability criteria are presented by constructing a novel Lyapunov-Krasovskii functional. Moreover, the results are further extended to the delayed stochastic HNNs with parameter uncertainties. The main idea is based on the delay partitioning technique, which differs greatly from most existing results and reduces conservatism. Numerical examples are provided to illustrate the effectiveness and less conservativeness of the developed techniques.