Ergodic chaos, learning and sunspot equilibrium

Abstract

In this paper we construct sunspot equilibria that arise from chaotic deterministic dynamics. These equilibria are stationary and have absolutely continuous stationary measures. We prove that they can be learned by a simple rule based on the histograms of past state variables. This work gives a theoretical justification for complex deterministic models that might compete with stochastic models to explain real data. Also we prove the stochastic stability of the indeterminate equilibrium.