NON PARAMETRIC-ESTIMATION OF THE CHAOTIC FUNCTION AND LYAPUNOV EXPONENTS OF A DYNAMICAL SYSTEM

Let (X(t)), t epsilon Z be a R(s)-valued stochastic process defined by a discrete time dynamical system as X(t) = phi (X(t-1)), where phi is some non linear function preserving a probability measure, say mu. We assume that phi is a chaotic transformation, therefore with positive Lyapunov exponents. We estimate phi and these, with kernel method for the I-egression. The estimates are consistent and the convergence rare of phi up to a logarithm is obtained.