Mean-Field Limits Beyond Ordinary Differential Equations [chapter]

Luca Bortolussi, Nicolas Gast
2016 Lecture Notes in Computer Science  
We study the limiting behaviour of stochastic models of populations of interacting agents, as the number of agents goes to infinity. Classical mean-field results have established that this limiting behaviour is described by an ordinary differential equation (ODE) under two conditions: (1) that the dynamics is smooth; and (2) that the population is composed of a finite number of homogeneous sub-populations, each containing a large number of agents. This paper reviews recent work showing what
more » ... ens if these conditions do not hold. In these cases, it is still possible to exhibit a limiting regime at the price of replacing the ODE by a more complex dynamical system. In the case of non-smooth or uncertain dynamics, the limiting regime is given by a differential inclusion. In the case of multiple population scales, the ODE is replaced by a stochastic hybrid automaton.
doi:10.1007/978-3-319-34096-8_3 fatcat:joi46epaa5hbhml4h4radenkc4