Before revision:  After bounding these solutions in time , we prove a rare type of convergence result, towards c\`adl\`ag exit-time limits, on Skorokhod' s M_1 topology. One immediate corollary of this limiting result is a weak connection between the time-averaged CIR process and  the inverse-Gaussian L\'evy subordinator .
After revision:  After bounding these solutions in time , meaning they need not have any spatial regularity properties such as Holder continuity. They are however strictly increasing in time, thus temporally asymmetric. When sensible initial values are chosen, IVP solutions are also strictly increasing, and the inverse-Gaussian L\'evy subordinator .