  We prove convergence to a Levy process for a class of dispersing billiards
with cusps. For such examples, convergence to a stable law was proved by Jung &
Zhang. For the corresponding functional limit law, convergence is not possible
in the usual Skorohod J_1 topology. Our main results yield elementary geometric
conditions for convergence (i) in M_1, (ii) in M_2 but not M_1.
  In general, we show for a large class of nonuniformly hyperbolic systems how
to deduce functional limit laws once convergence to the corresponding stable
law is known.
