  We consider the asymmetric exclusion process with a driven tagged particle on
Z which has different jump rates from other particles and show that the tagged
particle can have a ballistic behavior when the non-tagged particles have
non-nearest-neighbor jump rates. We show the existence of some non-trivial
invariant measures for the environment process viewed from the tagged particle.
Our arguments are based on coupling, the martingale approach, and analyzing
currents through fixed bonds.
