Recent developments in nonlinear stochastic modelling of social processes

After a brief review of social applications of Markov chains, the paper discusses nonlinear (“interactive”) Markov models in discrete and continuous time. The rather subtle relationship between the deterministic and stochastic versions of such models is explored by means of examples. It is shown that the behaviour of nonlinear systems over time periods of practical interest depends critically on the total size as well as on the system parameters. Particular attention is paid to strong and weak forms of quasi‐stationarity exhibited by stochastic systems.