  We consider a nonequilibrium process on a timeline with discrete sites which
evolves by a non-Markovian update rule in such a way that an active site at
time t activates one or several sites in the future at time t+dt. The time
intervals dt are distributed algebraically as dt^(-1-kappa), where 0<kappa<1 is
a control paramter. Depending on the activation rate, the system display a
nonequilibrium phase transition which may be interpreted as directed
percolation transition driven by temporal Levy flights in the limit of zero
space dimensions. The critical properties are investigated by extensive
numerical simulations and compared with field-theoretic predictions.
