A statistical model for cellular proliferation

The evolution of a biological system, like a cellular one, is analyzed by constructing a Markov process on a suitable state space. This is performed by the introduction of an infinitesimal generator for the Markov semi-group associated to this process. A measure valued process is then defined in a natural way and it is proved that his first moment satisfies the Sharpe-Lotka system in a distributional sense. Hence the study of the moments of the process is tried. An involved integral equation for the moment generating functional is derived.