In this paper, we present a new approach to system identification and stochastic adaptive control, by viewing these as problems in statistical learning theory. The main motivation for initiating such a program is that traditional stochastic identification methods provide asymptotic results, whereas statistical learning theory provides finite-time results. If system identification is to be combined with robust control theory to provide a sound mathematical basis for indirect adaptive control, it is essential to have finite-time estimates of the sort provided by statistical learning theory. As an illustration of this approach, a result is derived showing that in the case of input-output stable systems with fading memory, it is possible to adapt some standard arguments from statistical learning theory to provide finite-time estimates of the rate of convergence of the identified model to the true system.