  Large deviations for additive path functionals of stochastic dynamics and
related numerical approaches have attracted significant recent research
interest. We focus on the question of convergence properties for cloning
algorithms in continuous time, and establish connections to the literature of
particle filters and sequential Monte Carlo methods. This enables us to derive
rigorous convergence bounds for cloning algorithms which we report in this
paper, with details of proofs given in a further publication. The tilted
generator characterizing the large deviation rate function can be associated to
non-linear processes which give rise to several representations of the dynamics
and additional freedom for associated numerical approximations. We discuss
these choices in detail, and combine insights from the filtering literature and
cloning algorithms to compare different approaches and improve efficiency.
