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This brief addresses the stability analysis problem for stochastic neural networks (SNNs) with discrete interval and distributed time-varying delays. The interval time-varying delay is assumed to satisfy 0 < d ₁ ¿ d(t) ¿ d ₂ and is described as d ( t ) = d ₁ + h ( t ) with 0 ¿ h ( t ) ¿ d ₂ - d ₁ . Based on the idea of partitioning the lower bound d ₁ , new delay-dependent stability criteria are presented by constructing a novel Lyapunov-Krasovskii functional, which can guarantee the new stability conditions to be less conservative than those in the literature. The obtained results are formulated in the form of linear matrix inequalities (LMIs). Numerical examples are provided to illustrate the effectiveness and less conservatism of the developed results.