Optimal Policies for Convex Symmetric Stochastic Dynamic Teams and their Mean-Field Limit

Mean Field Limit for Stochastic Particle Systems

We review some classical and more recent results for the derivation of mean field equations from systems of many particles, focusing on the stochastic case where a large system of SDE’s leads to a McKean-Vlasov PDE as the number N of particles goes to infinity. Classical mean field limit results require that the interaction kernel be essentially Lipschitz. To handle more singular interaction ke...

Mean-field limit for the stochastic Vicsek model

We consider the continuous version of the Vicsek model with noise, proposed as a model for collective behavior of individuals with a fixed speed. We rigorously derive the kinetic mean-field partial differential equation satisfied when the number N of particles tends to infinity, quantifying the convergence of the law of one particle to the solution of the PDE. For this we adapt a classical coup...

Quantitative Determination Of Optimal Fiscal And Monetary Policies: A Stochastic Optimal Control Analysis For Iran

Convergence of Sample Path Optimal Policies for Stochastic Dynamic Programming

We consider the solution of stochastic dynamic programs using sample path estimates. Applying the theory of large deviations, we derive probability error bounds associated with the convergence of the estimated optimal policy to the true optimal policy, for finite horizon problems. These bounds decay at an exponential rate, in contrast with the usual canonical (inverse) square root rate associat...

Stochastic Mean-Field Limit: Non-Lipschitz Forces & Swarming

We consider general stochastic systems of interacting particles with noise which are relevant as models for the collective behavior of animals, and rigorously prove that in the mean-field limit the system is close to the solution of a kinetic PDE. Our aim is to include models widely studied in the literature such as the CuckerSmale model, adding noise to the behavior of individuals. The difficu...