This thesis has the aim of analyzing the situation of R&D expenditures distribution in European regions to evaluate the possibility of the presence of a distribution under a core-peripherical model on the basis of Krugman's theory. I studied the phenomenon through stochastic kernels, the method of analysis developed first by Quah to show intradistribution dynamics. The evidence shows the reduction in time of regional differences in R&D expenditures, with an increase of the number of regions with medium level of expenditures and the reduction of the number of low investment regions.