Mean field approach for a class of stochastic control systems

In this talk we introduce a model for stochastic control systems composed composed by a large number N of interacting objects who evolve randomly (according to a transition law) among a set of categories. Then we define the corresponding control problem. Due to a large number of objects in the system we appeal to the mean field approach, that propose us to analyze the proportion of objects occupying each category instead of focus in a single object. This leads us to define the so-called mean field control model and its respective problem, which under appropriate conditions, result in a model more tractable than the original, and the mean field optimal policy turns out to have good behavior in the original problem. To fix ideas of the elements mentioned in the models, we present an interesting application in forest management.