Although stochastic E-L (Eulerian-Langrangian) wave theory does not require random perturbation techniques in principle to provide solutions, in practice, ensemble expectations are usually resolved by perturbing the random medium. The fundamental concepts for the evaluation of wave functionals are first treated in one dimension, then a central limit theorem for Lagrangian functionals permits these concepts to be treated in three dimensional analysis via stochastic perturbation. The resultant relation for calculating the pertinent Eulerian ensemble expectation corresponding to the Lagrangian functional in question is shown to depend in a natural manner upon the Lagrangian path spreading and, in the case of a statistically isotropic medium, to reduce to the proper nonstochastic limit. Thence, stochastic E-L wave theory can be demonstrated via stochastic perturbation techniques applied to secular Lagrangian relations. In the stationary Markovian limit, the comparable Weiner integral results.