[en] A functional characterization of stochastic evolutions within the state spaces of commutative C*-algebras with identity is derived. Consequences concerning the structure of those linear evolution equations (master equations) that give occassion to stochastic evolutions are discussed. In part, these results generalize facts which are well-known from the finite dimensional classical case. Examples are given and some important particularities of the W*-case are developed. (author)