  In this paper we propose a wide class of truncated stochastic approximation
procedures with moving random bounds. While we believe that the proposed class
of procedures will find its way to a wider range of applications, the main
motivation is to accommodate applications to parametric statistical estimation
theory. Our class of stochastic approximation procedures has three main
characteristics: truncations with random moving bounds, a matrix valued random
step-size sequence, and dynamically changing random regression function. We
establish convergence and consider several examples to illustrate the results.
