  Extensive simulations are performed to study the persistence behavior of a
conserved lattice gas model exhibiting an absorbing phase transition from an
active phase into an inactive phase. Both the global and the local persistence
exponents are determined in two and higher dimensions. The local persistence
exponent obeys a scaling relation involving the order parameter exponent of the
absorbing phase transition. Furthermore we observe that the global persistence
exponent exceeds its local counterpart in all dimensions in contrast to the
known persistence behavior in reversible phase transitions.
