  We design a particle interpretation of Feynman-Kac measures on path spaces
based on a backward Markovian representation combined with a traditional mean
field particle interpretation of the flow of their final time marginals. In
contrast to traditional genealogical tree based models, these new particle
algorithms can be used to compute normalized additive functionals "on-the-fly"
as well as their limiting occupation measures with a given precision degree
that does not depend on the final time horizon.
  We provide uniform convergence results w.r.t. the time horizon parameter as
well as functional central limit theorems and exponential concentration
estimates. We also illustrate these results in the context of computational
physics and imaginary time Schroedinger type partial differential equations,
with a special interest in the numerical approximation of the invariant measure
associated to $h$-processes.
