Asymptotic inference for dynamical systems observed with error

Abstract

In this article, the effects of measuring a dynamical system with error are investigated. In particular, we assume that the measurement errors follow a distribution in the exponential family, and that the value of the underlying dynamical system determines the parameter of the measurement distribution. The key questions are whether two distinct initial conditions can be asymptotically distinguished and whether two distinct parameter values can be asymptotically distinguished. Results of the statistical theory are applied in the context of dynamical systems.