ABSTRACT
The Feynman-Kac models presented in Section 1.4.2, and further developed in Chapter 3, were defined in terms of Markov chain distributions, weighted by some potential functions. This description is particularly useful to model conditional distributions of Markov chains w.r.t. a collection of conditioning events. In this section, we present a natural and alternative interpretation of these models in terms of spatial branching processes. We also extend the Feynman-Kac methodology to branching models, equipped with spontaneous birth rates. These extended Feynman-Kac distribution flows are defined as in (1.41), by adding at every time step a possibly different positive measure.
