Large deviations for some non-standard telegraph processes

We prove large deviation principles for three non-standard telegraph processes. The first one is a damped model with velocity driven by Bernoulli trials studied in Crimaldi et al. (2013), and we obtain the same rate function obtained in De Gregorio and Macci (2014) for another damped telegraph process. The other telegraph processes are non-damped models and we assume suitable hypotheses: in a case the holding times have a general super-exponential distribution, in another case the change-of-direction number process satisfies a large deviation principle.