  In the following article we consider the time-stability associated to the
sequential Monte Carlo (SMC) estimate of the backward interpretation of
Feynman-Kac Formulae. This is particularly of interest in the context of
performing smoothing for hidden Markov models (HMMs). We prove a central limit
theorem (CLT) under weaker assumptions than adopted in the literature. We then
show that the associated asymptotic variance expression, for additive
functionals grows at most linearly in time, under hypotheses that are weaker
than those currently existing in the literature. The assumptions are verified
for some state-space models.
