Response probability density functions of Duffing-Van der Pol vibro-impact system under correlated Gaussian white noise excitations

► Non-smooth transformation is used to transform vibro-impact system to a new system. ► Response stationary PDFs are derived by using the stochastic averaging method. ► The validity of analytical PDFs is verified by the numerical simulations. ► Stochastic bifurcations are also explored in the paper.