  We study the rate of convergence of linear two-time-scale stochastic
approximation methods. We consider two-time-scale linear iterations driven by
i.i.d. noise, prove some results on their asymptotic covariance and establish
asymptotic normality. The well-known result [Polyak, B. T. (1990). Automat.
  Remote Contr. 51 937-946; Ruppert, D. (1988). Technical Report 781, Cornell
Univ.] on the optimality of Polyak-Ruppert averaging techniques specialized to
linear stochastic approximation is established as a consequence of the general
results in this paper.
