In this article we are interested in the dynamical behavior of the mean field description of neural networks with random synaptic weights and stochastic inputs. Unlike other authors, we consider this problem as a \emph{measure problem}. From this point of view we address the question of existence and uniqueness of solutions of dynamic mean field equations describing the behavior of the neural network in the large size limit. To this purpose, we introduce a new metric on the set of stochastic processes for which this set is complete. In this framework, we use the standard theory of fixed points in complete spaces to prove existence and uniqueness of solutions. This framework gives us a direct method to compute explicitly these solutions, and allows us to generalize previous results to more general models. We also consider the problem of existence and uniqueness of stationary solutions which have been previously studied essentially using local or numerical methods. We finally give some examples of results obtained by the numerical technique proposed.