On the two-filter approximations of marginal smoothing distributions in   general state space models
  A prevalent problem in general state space models is the approximation of the smoothing distribution of a state conditional on the observations from the past, the present, and the future. The aim of this paper is to provide a rigorous analysis of such approximations of smoothed distributions provided by the two-filter algorithms. We extend the results available for the approximation of smoothing distributions to these two-filter approaches which combine a forward filter approximating the filtering distributions with a backward information filter approximating a quantity proportional to the posterior distribution of the state given future observations. 
Thi Ngoc Minh Nguyen (LTCI), Sylvain Le Corff (LM-Orsay), Eric   Moulines (CMAP)
math.ST math.PR stat.TH