On the decomposition of stochastic cellular automata

In this paper we present two interesting properties of stochastic cellular automata that can be helpful in analyzing the dynamical behavior of such automata. The first property allows calculating cell-wise probability distributions over the state set of a stochastic cellular automaton, i.e. images that show the average state of each cell during the stochastic cellular automaton evolution. The second property shows that stochastic cellular automata are equivalent to so-called stochastic mixtures of deterministic cellular automata. By means of this property, any stochastic cellular automaton can be decomposed into a set of deterministic systems, each of which contributes to the behavior of the stochastic system.