Dan Crisan, Jessica Gaines, and Terry Lyons, as well as Pierre Del Moral, and Terry Lyons, created branching-type particle techniques with various population sizes around the end of the 1990s. P. Del Moral, A. Guionnet, and L. Miclo made more advances in this subject in 2000. Pierre Del Moral and Alice Guionnet proved the first central limit theorems in 1999, and Pierre Del Moral and Laurent Miclo proved them in 2000. The first uniform convergence results concerning the time parameter for particle filters were developed at the end of the 1990s by Pierre Del Moral and Alice Guionnet. The first rigorous analysis of genealogical tree-ased particle filter smoothers is due to P. Del Moral and L. Miclo in 2001