The lion's share of this chapter is devoted to the construction of equilibria for mean field
games with a common noise. We develop a general two-step strategy for the search of weak …

We rigorously prove a central limit theorem for neural network models with a single hidden
layer. The central limit theorem is proven in the asymptotic regime of simultaneously (A) …

Effective Dynamics of Stochastic Partial Differential Equations focuses on stochastic partial
differential equations with slow and fast time scales, or large and small spatial scales. The …

Stochastic Filtering Theory uses probability tools to estimate unobservable stochastic
processes that arise in many applied fields including communication, target-tracking, and …

Mean field games (MFGs) describe the limit, as n tends to infinity, of stochastic differential
games with n players interacting with one another through their common empirical …

We force uniqueness in finite state mean field games by adding a Wright–Fisher common
noise. We achieve this by analyzing the master equation of this game, which is a degenerate …

We consider an n-player symmetric stochastic game with weak interactions between the
players. Time is continuous, and the horizon and the number of states are finite. We show …

The present volume analyzes mathematical models of time-dependent physical phenomena
on three levels: microscopic, mesoscopic, and macroscopic. We provide a rigorous …

We consider the asymptotic behaviour of the fluctuations for the empirical measures of
interacting particle systems with singular kernels. We prove that the sequence of fluctuation …

We consider weakly interacting diffusions on time varying random graphs. The system
consists of a large number of nodes in which the state of each node is governed by a …