  The purpose of this paper is to explore mathematical aspects associated with
the application of the direct interaction approximation (DIA) (Kraichnan
[1],[2]) to the non-Markovianized stochastic models in the turbulence problem.
This process is shown to lead to a functional equation, and construction of
solutions of this equation is addressed within the framework of a continued
fraction representation. The relation of the DIA solution to the perturbative
solution is discussed. The DIA procedure is applied to the problem of wave
propagation in a random medium, which is described by a stochastic differential
equation, with the characteristics of the medium represented by stochastic
coefficients. The results are compared with those given by the perturbative
procedure.
