Mathematics 797AB - ST-Agent Based Models

In this class we will discuss the mathematical and physical foundations of agent-based models and their applications to a large number of fields, for example statistical mechanics, evolutionary game theory, economics and social sciences, bio-chemical networks, and others. We will cover discrete probabilistic models on lattices as well as systems described by stochastic differential equations. We will develop some the mathematical foundations of the subject (Markov processes) and the necessary tools to understand the long-time behavior of such systems (ergodic theory). We will study various limits in which we obtain reduced description of stochastic systems at meso- or macro-scale using ODE's, SDE's, or PDE's as well as other coarse-graining procedures. We will also be interested in the issues of parameter identification and uncertainty quantification for such models as well as efficient numerical implementation of the models.