  We consider a general method for the approximation of the distribution of a
process conditioned to not hit a given set. Existing methods are based on
particle system that are failable, in the sense that, in many situations , they
are not well defined after a given random time. We present a method based on a
new particle system which is always well define. Moreover , we provide
sufficient conditions ensuring that the particle method converges uniformly in
time. We also show that this method provides an approximation method for the
quasi-stationary distribution of Markov processes. Our results are illustrated
by their application to a neutron transport model.
