Convergence of Learning Algorithms without a Projection Facility

Drawing upon recent contributions in the statistical literature, we present new results on the convergence of recursive, stochastic algorithms which can be applied to eonomic models with learning and which generalize previous results. The formal results provide probability bounds for convergence which can be used to describe the local stability under learning of rational expectations equilibria in stochastic models. Economic examples include local stability in a multivariate linear model with multiple equilibria and global convergence in a model with a unique equilibrium.