We consider a class of second-order degenerate kinetic operators \(\mathscr {L}\) in the framework of special relativity. We first describe \(\mathscr {L}\) as a Hörmander operator which is invariant with respect to Lorentz transformations. Then we prove a Lorentz-invariant Harnack type inequality, and we derive accurate asymptotic lower bounds for positive solutions to \(\mathscr {L}f = 0\) . As a consequence, we obtain a lower bound for the density of the relativistic stochastic process associated with \(\mathscr {L}\) .
