%O Preprint. 
Submitted for publication.
%I IMT Institute for Advanced Studies Lucca
%A Irene Crimaldi
%A Antonio Di Crescenzo
%A Antonella Iuliano
%A Barbara Martinucci
%T A generalized telegraph process with velocity driven by random trials
%D 2012
%L eprints1346
%X We consider a random trial-based telegraph process, which describes a motion on the real line with two constant velocities along opposite directions. At each epoch of the underlying counting process the new velocity is determined by the outcome of a random trial. Two schemes are taken into account: Bernoulli trials and classical P?lya urn trials. We investigate the probability law of the process and the mean of the velocity of the moving particle. We finally discuss two cases of interest: (i) the case of Bernoulli trials and intertimes having exponential distributions with linear rates (in which, interestingly, the process exhibits a logistic stationary density with non-zero mean), and (ii) the case of P?lya trials and intertimes having first Gamma and then exponential distributions with constant rates.