  We extend quantum trajectory theory to encompass the evolution of a large
class of open quantum systems interacting with an environment at {arbitrary
coupling strength}. Specifically, we prove that general time-local quantum
master equations admit an unraveling described by ordinary jump-stochastic
differential equations. The sufficient condition is to weigh the 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 quantum trajectories at strong
system-environment coupling.
  Our result proves the existence of a Markovian quantum trajectory picture in
the Hilbert space of the system for completely bounded divisible dynamical
maps. Furthermore, our result provides a new avenue to numerically integrate
systems with large numbers of degrees of freedom by naturally extending the
existing theory.
