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Automatica, ISSN 0005-1098, 12/2017, Volume 86, pp. 104 - 109
Journal Article
Journal de mathématiques pures et appliquées, ISSN 0021-7824, 06/2015, Volume 103, Issue 6, pp. 1441 - 1474
In his lectures at College de France, P.L. Lions introduced the concept of Master equation, see [8] for Mean Field Games. It is introduced in a heuristic... 
Linear quadratic problems | Master equation | Mean Field Games | Stochastic HJB equations | Stochastic maximum principle | Mean Field type control problems | Mean field type control problems | Mean field games | MATHEMATICS | MATHEMATICS, APPLIED | Game theory | Analysis
Journal Article
Physical Review C - Nuclear Physics, ISSN 0556-2813, 06/2011, Volume 83, Issue 6
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 10/2018, Volume 275, Issue 7, pp. 1603 - 1649
In this paper the Hartree equation is derived from the N-body Schrödinger equation in the mean-field limit, with convergence rate estimates that are uniform in... 
Hartree equation | Classical limit | Mean-field limit | Schrödinger equation | MATHEMATICS | Schrodinger equation | QUANTUM | DYNAMICS
Journal Article
Archive for Rational Mechanics and Analysis, ISSN 0003-9527, 1/2017, Volume 223, Issue 1, pp. 57 - 94
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 08/2017, Volume 369, Issue 8, pp. 5467 - 5523
mean-field stochastic differential equations with deterministic coefficients. Time-inconsistency feature of the problems is carefully investigated. Both... 
Equilibrium solution | N-person differential games | Time-inconsistency | Mean-field stochastic differential equation | Riccati equation | Linear-quadratic optimal control | Lyapunov equation | MATHEMATICS | time-inconsistency | linear-quadratic optimal control | INCONSISTENCY | GAMES | equilibrium solution | INVESTMENT
Journal Article
Reviews in Mathematical Physics, ISSN 0129-055X, 02/2015, Volume 27, Issue 1, p. 1550003
Using a new method [19], it is possible to derive mean field equations from the microscopic N body Schrödinger evolution of interacting particles without using... 
Gross-Pitaevskii | NLS | mean field | RIGOROUS DERIVATION | NONLINEAR SCHRODINGER | DYNAMICS | PHYSICS, MATHEMATICAL
Journal Article
Discrete and Continuous Dynamical Systems- Series A, ISSN 1078-0947, 01/2019, Volume 39, Issue 1, pp. 131 - 155
In his classical work on synchronization, Kuramoto derived the formula for the critical value of the coupling strength corresponding to the transition to... 
Graph limit | Mean field limit | Synchronization | Random graph | MATHEMATICS, APPLIED | random graph | STABILITY | CONSENSUS | LIMIT | NETWORKS | ARRAYS | INCOHERENCE | MATHEMATICS | DYNAMICS | synchronization | graph limit | SYSTEMS | COUPLED PHASE OSCILLATORS
Journal Article
Stochastic Processes and their Applications, ISSN 0304-4149, 2009, Volume 119, Issue 10, pp. 3133 - 3154
Journal Article
Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 03/2020, Volume 43, Issue 4, pp. 1901 - 1914
In this paper, we prove the global existence of the weak solution to the mean field kinetic equation derived from the N‐particle Newtonian system. For L1∩L∞... 
mean field limit | Vlasov‐like equations | partial differential equations | MATHEMATICS, APPLIED | VLASOV-POISSON SYSTEM | MATERIAL FLOW | Vlasov-like equations | MODEL | PROPAGATION | HIERARCHY | Kinetic equations
Journal Article
Nuclear Physics, Section A, ISSN 0375-9474, 2010, Volume 837, Issue 3, pp. 210 - 254
A statistical model for the equation of state and the composition of supernova matter is presented. It consists of an ensemble of nuclei and interacting... 
Nuclear statistical equilibrium | Supernovae | Excluded volume | Liquid–gas phase transition | Nuclear matter | Equation of state | Liquid-gas phase transition | NEUTRON EQUATION | PHASE-TRANSITIONS | PHYSICS, NUCLEAR | HOT | DENSITY | RATES | SHOCK | NUCLEAR-MATTER | MEAN-FIELD THEORY | RADII | CORE-COLLAPSE SUPERNOVAE
Journal Article
Stochastic Processes and their Applications, ISSN 0304-4149, 10/2019, Volume 129, Issue 10, pp. 3859 - 3892
We consider a system of forward–backward stochastic differential equations (FBSDEs) with monotone functionals. We show that such a system is well-posed by the... 
Monotone functional | Mean field games with common noise | Mean field FBSDE with conditional law | Forward–backward stochastic differential equations | STATISTICS & PROBABILITY | Forward-backward stochastic differential equations | Differential equations
Journal Article
SIAM Journal on Control and Optimization, ISSN 0363-0129, 2013, Volume 51, Issue 4, pp. 2809 - 2838
Journal Article
SIAM Journal on Numerical Analysis, ISSN 0036-1429, 2018, Volume 56, Issue 4, pp. 2672 - 2697
In this work, we propose a class of explicit theta-schemes for solving mean-field backward stochastic differential equations. We first prove a rigorous... 
Θ-schemes | Mean-field backward stochastic differential equation | Error estimates | MATHEMATICS, APPLIED | GAMES | mean-field backward stochastic differential equation | SDES | MCKEAN-VLASOV | theta-schemes | error estimates
Journal Article
Automatica, ISSN 0005-1098, 06/2014, Volume 50, Issue 6, pp. 1565 - 1579
Journal Article
Science, ISSN 0036-8075, 11/2002, Volume 298, Issue 5598, pp. 1592 - 1596
Journal Article