Abstract
The nonlinear problem of the behavior of decaying, isothermal, second-order reactions is posed stochastically. The exact solution, using an initial multivariate normal probability distribution, is compared with various closure approximations that have been employed in the study of turbulence. Kraichnan's direct-interaction hypothesis provides a satisfactory discription of the behavior of single-point functions and of the covariance of the concentration field as does the joint normal distribution hypothesis. However, the former is slightly superior even in this problem in which the energetic difficulties of the latter are not apparent.