Some results pertaining to co-dimension two stochastic bifurcations are presented. The
normal form associated with non-semi-simple double-zero eigenvalues is considered. The
method of stochastic averaging applicable for singularly perturbed stochastic differential
equations is used to further reduce the problem to a one-dimensional diffusion process.
Probability density, most probable values, stability conditions in probability, and mean exit
times are obtained for the reduced system.