This paper addresses the stability of stochastic delayed recurrent neural networks (SDRNNs), identifying challenges in existing scalar methods, which suffer from strong assumptions and limited applicability. Three key innovations are introduced: (1) weakening noise perturbation conditions by extending diagonal matrix assumptions to non-negative definite matrices; (2) establishing criteria for both mean-square exponential stability and almost sure exponential stability in the absence of input; (3) directly handling complex structures like time-varying delays through matrix analysis. Compared with prior studies, this approach yields broader stability conclusions under weaker conditions, with numerical simulations validating the theoretical effectiveness.