  We study approximations of evolving probability measures by an interacting
particle system. The particle system dynamics is a combination of independent
Markov chain moves and importance sampling/resampling steps. Under global
regularity conditions, we derive non-asymptotic error bounds for the particle
system approximation. In a few simple examples, including high dimensional
product measures, bounds with explicit constants of feasible size are obtained.
Our main motivation are applications to sequential MCMC methods for Monte Carlo
integral estimation.
