Dipartimento di Scienze Statistiche

The aim of this paper is to derive large deviation results for random motions with finite velocity. We start with large deviation principles for the telegraph process with drift: we consider both non-conditional distributions and conditional distributions, and we compare the speeds of convergence with inequalities between rate functions. The same results are presented for the random flights in R^2 and in R^4 which represent a multidimensional version of the telegraph process. Other large deviation principles in this paper concern the non-conditional distributions for an inhomogeneous telegraph process and for a planar random motion with orthogonal directions.