  We introduce a generalization of the Adaptive Multilevel Splitting algorithm
in the discrete time dynamic setting, namely when it is applied to sample rare
events associated with paths of Markov chains. By interpreting the algorithm as
a sequential sampler in path space, we are able to build an estimator of the
rare event probability (and of any non-normalized quantity associated with this
event) which is unbiased, whatever the choice of the importance function and
the number of replicas. This has practical consequences on the use of this
algorithm, which are illustrated through various numerical experiments.
