A new model of Campi Flegrei inflation and deflation episodes based on Brownian motion driven by the telegraph process

In this paper, a stochastic model has been proposed to describe the vertical motions in the volcanic region named Campi Flegrei. The model consists of a Brownian motion process driven by a generalized telegraph process. The knowledge of the probability law of this process allows to perform a quantitative investigation on some basic parameters regulating the inflation/deflation processes, such as velocities and time constants. The statistical analysis is based on linear regression with constraints. A prediction of the ground displacement and the change of tendency for future time instants is also carried out. Finally, a statistical test on the Brownian component of the process confirms the goodness of the model.