Continuous approximation of collective systems behaviour: a tutorial

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