Repository landing page
Mean-Field Limits Beyond Ordinary Differential Equations
Abstract
16th International School on Formal Methods for the Design of Computer, Communication, and Software Systems, SFM 2016, Bertinoro, Italy, June 20-24, 2016, Advanced LecturesInternational audienceWe 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 happens 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- info:eu-repo/semantics/bookPart
- Book sections
- Population models
- Markov chain
- Mean-field limits
- Dif-ferential inclusions
- Hybrid systems
- [INFO.INFO-NI]Computer Science [cs]/Networking and Internet Architecture [cs.NI]
- [INFO.INFO-PF]Computer Science [cs]/Performance [cs.PF]
- [MATH]Mathematics [math]
- [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
- [MATH.MATH-PR]Mathematics [math]/Probability [math.PR]