Cellular Automata and Riccati Equation Models for Diffusion of Innovations

In order to recognize different local diffusions, Cellular Automata models (CA) are a recent example of the trial to fill in this shortage. Boccara and Fuks (1997) and Boccara (2004) have proposed an interesting representation of special CA. In this paper we briefly introduce a class of CA and, in particular, we approximate a natural extension (BFG) of the Boccara and Fuks (1997) model with a continuous Riccati representation of the corresponding discrete time equation. We solve, in closed form, a quite general non autonomous Riccati equation and apply previous results to BFG by examining statistical aspects concerned with inference.