  We show that general time-local quantum master equations admit an unravelling
in quantum trajectories with jumps. The sufficient condition is to weigh state
vector Monte Carlo averages by a probability pseudo-measure which we call the
"influence martingale". The influence martingale satisfies a $ 1d $ stochastic
differential equation enslaved to the ones governing the quantum trajectories.
Our interpretation is that the influence martingale models interference effects
between distinct realizations of the quantum trajectories at strong
system-environment coupling.
  If the master equation generates a completely positive dynamical map, there
is no interference. In such a case the influence martingale becomes positive
definite and the Monte Carlo average straightforwardly reduces to the well
known unravelling of completely positive divisible dynamical maps.
