  We investigate the application of the Adaptive Multilevel Splitting algorithm
for the estimation of tail probabilities of solutions of Stochastic
Differential Equations evaluated at a given time, and of associated temporal
averages.
  We introduce a new, very general and effective family of score functions
which is designed for these problems. We illustrate its behavior on a series of
numerical experiments. In particular, we demonstrate how it can be used to
estimate large deviation rate functionals for the longtime limit of temporal
averages.
