  Two time scale stochastic approximation algorithms emulate singularly
perturbed deterministic differential equations in a certain limiting sense,
i.e., the interpolated iterates on each time scale approach certain
differential equations in the large time limit when viewed on the `algorithmic
time scale' defined by the corresponding step sizes viewed as time steps. Their
fluctuations around these deterministic limits, after suitable scaling, can be
shown to converge to a Gauss-Markov process in law for each time scale. This
turns out to be a linear diffusion for the faster iterates and an ordinary
differential equation for the slower iterates.
