A new on-line learning model

We introduce a new supervised learning model that is a nonhomogeneous Marko v process and investigate its properties. We are interested in conditions t hat ensure that the process converges to a "correct state," which means tha t the system agrees with the teacher on every "question." We prove a suffic ient condition for almost sure convergence to a correct state and give seve ral applications to the convergence theorem. In particular, we prove severa l convergence results for well-known learning rules in neural networks.