Strong consistency of recursive identification by no use of persistent excitation condition (Q1100177)

For the discrete-time stochastic system without monitoring, the strong consistency of the estimate given by the stochastic gradient algorithm is considered when the persistent excitation condition is possibly not fulfilled. In addition, the convergence rate is given for a specific class of system noises, while in the adaptive tracking case the convergence rate for the parameter estimates as well as the tracking error are obtained when the reference signal is disturbed by a ``dither''.