Applied stochastic approximation algorithms in Hilbert space

This paper considers the theory of stochastic approximation in a Hilbert space setting for applicable purposes with emphasis in system identification. The algorithms investigated here converge in quadratic mean and with probability 1 and are less restrictive, from the application viewpoint, than the original works on stochastic approximation theory. This approach supplies a suitable class of algorithms satisfying the convergence requirements, without compromising the system identification applicability.