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The stability of stochastic Hopfield neural networks, in the Abe formulation, is studied. The aim is to determine whether the ability of the deterministic system to solve combinatorial optimization problems is preserved after the addition of random noise. In particular, the stochastic stability of the attractor set is analyzed: vertices, which are feasible points of the problem, should be stable, whereas interior points, which are unfeasible, should be unstable. Conditions on the noise intensity are stated, so that these properties are guaranteed. This theoretical investigation establishes the foundations for practical application of stochastic networks to combinatorial optimization.