Convergence of Learning Algorithms Without a Projection Facility

Drawing upon recent contributions in the statistical literature, we present a new result on the convergence of recursive, stochastic algorithms which can be applied to economic models with learning. The formal result provides probability bounds for convergence which can be used to describe the local stability under learning of rational expectations equilibria. Our treatment also generalizes previous results by permitting the state variable to follow a nonlinear Markov process. Two economic applications are discussed