Correction terms for parametric white noise processes. Gaussian, Poissonian and α-stable

In this work, the important rules of the stochastic differential calculus, when the external and parametric (or multiplicative) excitations are modeled as Gaussian white noise processes, are generalized to the case of non-Gaussian white noise excitations. This extension began some years ago, when the classical Gaussian stochastic differential calculus was generalized to thePoisson delta-correlated actions. In the present work, the extension has been completed considering the more general class of white noise excitations, which are α-stable Lévy white noises. It is shown that, in the case of parametric excitations, this extension also regards the correction terms necessary for using the Ito-type integration. These results have been possible thanks to the evidence that all the white processes here considered belong to a class of processes (the motion ones), whose formal derivative is just an element of the white noise class.