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We introduce an extension of the classic Discrete Event System Specification (DEVS) formalism that includes stochastic features. Based on the use of the probability spaces theory we define the stochastic DEVS (STDEVS) specification, which provides a formal framework for modeling and simulation of general non-deterministic discrete event systems. The main theoretical properties of the STDEVS framework are treated, including a new definition of legitimacy of models in the stochastic context and a proof of STDEVS closure under coupling. We also illustrate the new stochastic modeling capabilities introduced by STDEVS and their relation with those found in classic DEVS. Practical simulation examples are given involving performance analysis of computer systems and hybrid modeling of networked control systems, applications where the modeling of stochastic components is vital.