  We consider ensembles of trajectories associated with large deviations of
time-integrated quantities in stochastic models. Motivated by proposals that
these ensembles are relevant for physical processes such as shearing and glassy
relaxation, we show how they can be generated directly using auxiliary
stochastic processes. We illustrate our results using the Glauber-Ising chain,
for which biased ensembles of trajectories can exhibit ferromagnetic ordering.
We discuss the relation between such biased ensembles and quantum phase
transitions.
