Ricerc@Sapienza

We consider a dynamical system with small noise for which the drift is parametrized by a finite dimensional parameter. For this model, we consider minimum distance estimation from continuous time observations under lp-penalty imposed on the parameters in the spirit of the Lasso approach, with the aim of simultaneous estimation and model selection. We study the consistency and the asymptotic distribution of these Lasso-type estimators for different values of p. For p = 1, we also consider the adaptive version of the Lasso estimator and establish its oracle properties.

In the last decades there has been an increasing interest in studying degeneracies in BVPs such as those due to highly irregular domains as in the case of fractal boundaries or interfaces, or due to the presence of composite media . Other singularities arise when studying evolution problems with dynamical boundary conditions in fractal domains. In all these cases it is important, also in view of numerical approximations, to approximate these wild geometries by smoother ones and to study the convergence of approximating functions to the limit fractal one.