We make a stochastic analysis of both deterministic and stochastic cellular automata. The theory uses a mesoscopic view, i.e. it works with probabilities instead of individual configurations used in micro-simulations. We make an exact analysis by using the theory of Markov processes. This can be done for small problems only. For larger problems we approximate the distribution by products of marginal distributions of low order. The approximation use new developments in efficient computation of probabilities based on factorizations of the distribution. We investigate the popular voter model. We show that for one dimension the bifurcation at α = 1/3 is an artifact of the mean-field approximation.