  The aim of this paper is to tackle part of the program set by Diekmann et al.
in their seminal paper Diekmann et al. (2001). We quote "It remains to
investigate whether, and in what sense, the nonlinear determin-istic model
formulation is the limit of a stochastic model for initial population size
tending to infinity" We set a precise and general framework for a stochastic
individual based model : it is a piecewise deterministic Markov process defined
on the set of finite measures. We then establish a law of large numbers under
conditions easy to verify. Finally we show how this applies to old and new
examples.
