Nonparametric estimation of the chaotic function and the invariant measure of a dynamical system
Résumé
Let (Xt), Image be Image valued stochastic process defined by a discrete time dynamical system as Xt = phi(Xt−1, T = 1,2,..., where phi is some nonlinear function preserving a probability measure say μ, we estimate phi and the density -f of μ without using special condition on the analytical form of phi, with nonparametric methods and some convergence rates are given.