ABSTRACT
Feynman-Kac models on path spaces and their genealogical tree based particle approximations have been discussed in several places in earlier chapters of the book. Roughly speaking, up to natural state space enlargement, we have seen that the Feynman-Kac measures (Γn,Qn) defined in (1.38) and (1.37) can also be interpreted as the n-th time marginals of a Feynman-Kac model with a reference Markov chain associated with historical processes. In this interpretation, the genealogical tree based approximations of the measures (Γn,Qn) can be interpreted as the mean field Feynman-Kac particle model associated with an historical process. In this interpretation, Feynman-Kac models on path spaces and their genealogical tree based approximations are mathematically equivalent to the particle density profiles developed in Chapter 14.
