Impulsive systems are a very flexible class of systems that can be used to represent switched and sampled-data systems. We propose to extend here the previously obtained results on deterministic impulsive systems to the stochastic setting. The concepts of mean-square stability and dwell-times are utilized in order to formulate relevant stability conditions for such systems. These conditions are formulated as convex clock-dependent linear matrix inequality conditions that are applicable to robust analysis and control design, and are verifiable using discretization or sum of squares techniques. Stability conditions under various dwell-time conditions are obtained and non-conservatively turned into state feedback stabilization conditions. The results are finally applied to the analysis and control of stochastic sampled-data systems. Several comparative examples demonstrate the accuracy and the tractability of the approach. (C) 2016 Elsevier Ltd. All rights reserved.