Continuous approximation of collective systems behaviour: a tutorial

In this paper we present an overview of the field of deterministic approximation of Markov processes, both in discrete and continuous times. We will discuss mean field approximation of discrete time Markov chains and fluid approximation of continuous time Markov chains, considering the cases in which the deterministic limit process lives in continuous time or discrete time. We also consider some more advanced results, especially those relating to the limit stationary behaviour. We assume a knowledge of modelling with Markov chains, but not of more advanced topics in stochastic processes.