In a recent paper we proposed a new definition of Boltzmannian equilibrium and showed that in the case of deterministic dynamical systems the new definition implies the standard characterisation of equilibrium as the largest macrostate but without suffering from its well-known problems and limitations. We now generalise this result to stochastic systems and show that the same implication holds. We then discuss an existence theorem for equilibrium states and illustrate with a number of examples how the theorem works. Finally, fist steps towards understanding the relation between Boltzmannian and Gibbsian equilibrium are made.