From the Convex addition of two independent stochastic vectors, one of them being the output of a Markov chain, the convex stochastic model is defined. Emphasis is on the Moore version of the model. Response equations are given. The relation between this model and the stochastic sequential machine is found. Paralleling the ideas used in systems approach a zero input machine is defined, which plays a very important role in determining the special characteristics of the convex stochastic machine. Equivalence, state minimization, and asymptotic behavior are among the problems discussed.