Consistent estimation of a dynamical map

Estimation of a nonlinear map F governing the evolution of an observed dynamical system as considered in two specific models. In the first model, F is successively applied to a fixed initial vector in the absence of noise, so that the the observed states of the system constitute a trajectory off. In the second, dynamical noise model, the system is perturbed by independent noise between each application off. Estimates off are proposed for each model, and are shown to be consistent under general conditions. No assumptions are made regarding mixing rates of the observations. Both continuous and general measurable maps F are considered.