In this article, the authors put forward another viewpoint which shows how a "small noise" (which may be Gaussian) can cause great fluctuations because of the unstable structure of the model skeleton (i.e. its deterministic part) and whihc permits nevertheless to undertake forecast methods in...

We study the estimation of the marginal probability density function of an observable process associated to a weak bernoulli deterministic dynamical system. We use the Parzen-Rosenblatt naive kernel estimator and state conditions under which it is consistent in quadratic mean. We then discuss...

We present a general framework for understanding the transition from local regular to global irregular (chaotic) bahaviour of nonlinear dynamical models in discrete time. The fundamental mechanism is the unfolding of quadratic tangencies between the stable and the unstable manifolds of periodic...