Related papers: Mean field limits for discrete-time dynamical syst…
Financial markets and more generally macro-economic models involve a large number of individuals interacting through variables such as prices resulting from the aggregate behavior of all the agents. Mean field games have been introduced to…
This paper deals with the derivation of the mean-field limit for multi-agent systems on a large class of sparse graphs. More specifically, the case of non-exchangeable multi-agent systems consisting of non-identical agents is addressed. The…
We study the problem of mean-field control when the state dynamics are given by general systems of forward-backward stochastic differential equations (FBSDEs) with heterogeneous mean-field interactions. Firstly, we introduce a novel…
Validity of the mean-field approach to open system dynamics in the optical cavity system is examined. It is rigorously shown that the mean-field approach is justified in the thermodynamic limit. The result is applicable to nonequilibrium…
We introduce a novel framework to model and solve mean-field game systems with nonlocal interactions. Our approach relies on kernel-based representations of mean-field interactions and feature-space expansions in the spirit of kernel…
The finite horizon $H_2/H_\infty$ control problem of mean-field type for discrete-time systems is considered in this paper. Firstly, we derive a mean-field stochastic bounded real lemma (SBRL). Secondly, a sufficient condition for the…
A cellular automaton model is presented for random walkers with biologically motivated interactions favoring local alignment and leading to collective motion or swarming behavior. The degree of alignment is controlled by a sensitivity…
Consider the class of Ensemble Square Root filtering algorithms for the numerical approximation of the posterior distribution of nonlinear Markovian signals partially observed with linear observations corrupted with independent measurement…
In this article, we propose a new unifying framework for the investigation of multi-agent control problems in the mean-field setting. Our approach is based on a new definition of differential inclusions for continuity equations formulated…
The synthesis of control laws for interacting agent-based dynamics and their mean-field limit is studied. A linearization-based approach is used for the computation of sub-optimal feedback laws obtained from the solution of differential…
Collaborative multi-agent robotic systems where agents coordinate by modifying a shared environment often result in undesired dynamical couplings that complicate the analysis and experiments when solving a specific problem or task.…
The dynamical mean-field theory (DMFT) is a widely applicable approximation scheme for the investigation of correlated quantum many-particle systems on a lattice, e.g., electrons in solids and cold atoms in optical lattices. In particular,…
We consider a mean-field control problem in which admissible controls are required to be adapted to the common noise filtration. The main objective is to show how the mean-field control problem can be approximates by time consistent…
This paper investigates the use of transformers to approximate the mean-field dynamics of interacting particle systems exhibiting collective behavior. Such systems are fundamental in modeling phenomena across physics, biology, and…
This paper presents a mean-field control approach for Piecewise Deterministic Markov Processes (PDMPs), specifically designed for controlling a large number of agents. By modeling the interactions of a large number of agents through an…
We study a multi-agent mean field type control problem in discrete time where the agents aim to find a socially optimal strategy and where the state and action spaces for the agents are assumed to be continuous. The agents are only weakly…
When controlling multi-agent systems, the trade-off between performance and scalability is a major challenge. Here, we address this difficulty by using mean field games (MFGs), which is a framework that deduces the macroscopic dynamics…
This paper develops a linear programming approach for mean field games with reflected jump-diffusion dynamics. We first prove the equivalence between the mean field equilibria in the linear programming formulation and those in the weak…
We consider spatially extended systems of interacting nonlinear Hawkes processes modeling large systems of neurons placed in Rd and study the associated mean field limits. As the total number of neurons tends to infinity, we prove that the…
In this work, we explore some interesting details of the time-dependent regime of the long-range systems under mean-field approximation in comparison with the critical dynamics of the short-range systems. First, we discuss some mechanisms…