@techreport{eprints1346,
            type = {Technical Report},
           month = {September},
     institution = {IMT Institute for Advanced Studies Lucca},
            note = {Preprint. 
Submitted for publication.},
          author = {Irene Crimaldi and Antonio Di Crescenzo and Antonella Iuliano and Barbara Martinucci},
           title = {A generalized telegraph process with velocity driven by random trials},
            year = {2012},
             url = {http://eprints.imtlucca.it/1346/},
        abstract = {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{\`o}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{\`o}lya trials and intertimes having first Gamma and then exponential distributions with constant rates. }
}