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This paper proposes a stochastic-robust constructive interference (CI) precoding scheme for downlink multi-user MISO systems, assuming that channel state information (CSI) at the transmitter side (CSIT) is contaminated by Gaussian-distributed uncertainties. Our objective is to minimize the total transmit power under users’ quality-of-service constraints: formulating CI at each user with high probabilities for a given target signal-to-noise ratio (SINR). We first analyze the probability of CI under imperfect CSIT. A series of approximations are then developed, transforming the intractable stochastic CI constraints into determined convex constraints. The non-convex stochastic-robust CI power minimization (CIPM) problem is then converted into second-order cone programming. We show that we could create tightened or relaxed approximations by changing the parameters, enabling us to find upper-bounds and lower-bounds for the original stochastic CIPM problem. The best parameter values corresponding to the tightest upper and lower bounds are also discussed and obtained. Simulation results show that the proposed methods reasonably approximate the stochastic CIPM problem. Using the given parameter values, it can guarantee the required probability of CI for each user under acceptable channel uncertainties and outperform the existing robust CI precoding in terms of both transmit power and feasibility rate. The small gap between the upper and lower bounds also shows that the proposed method does not cause too much performance loss. [ABSTRACT FROM AUTHOR]