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Mean field type control problems, some Hilbert-space-valued FBSDES, and related equations
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Controlled measure-valued martingales: A viscosity solution approach
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Kolmogorov equations on the space of probability measures associated to the nonlinear filtering equation: the viscosity approach
Master Bellman equation in the Wasserstein space: Uniqueness of viscosity solutions
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Finite Dimensional Approximations of Hamilton–Jacobi–Bellman Equations for Stochastic Particle Systems with Common Noise
Mean-Field Limit for a Class of Stochastic Ergodic Control Problems
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Characterization of stochastic equilibrium controls by the Malliavin calculus
A Probabilistic Approach to Classical Solutions of the Master Equation for Large Population Equilibria
Jean-François Chassagneux, Dan Crisan and François Delarue Memoirs of the American Mathematical Society 280(1379) (2022) https://doi.org/10.1090/memo/1379
McKean–Vlasov Optimal Control: Limit Theory and Equivalence Between Different Formulations
Kai Cui, Wasiur R. KhudaBukhsh and Heinz Koeppl Chaos: An Interdisciplinary Journal of Nonlinear Science 32(11) (2022) https://doi.org/10.1063/5.0093758
Finite Dimensional Approximations of Hamilton--Jacobi--Bellman Equations in Spaces of Probability Measures
Wilfrid Gangbo, Sergio Mayorga and Andrzej Świeͅch SIAM Journal on Mathematical Analysis 53(2) 1320 (2021) https://doi.org/10.1137/20M1331135
Lattice approximations of the first-order mean field type differential games
Viscosity Solutions for Controlled McKean--Vlasov Jump-Diffusions
Matteo Burzoni, Vincenzo Ignazio, A. Max Reppen and H. M. Soner SIAM Journal on Control and Optimization 58(3) 1676 (2020) https://doi.org/10.1137/19M1290061
Closed-Loop Equilibrium for Time-Inconsistent McKean--Vlasov Controlled Problem
Extended Mean Field Control Problems: Stochastic Maximum Principle and Transport Perspective
Beatrice Acciaio, Julio Backhoff-Veraguas and René Carmona SIAM Journal on Control and Optimization 57(6) 3666 (2019) https://doi.org/10.1137/18M1196479
Numerical method for FBSDEs of McKean–Vlasov type
Jean-François Chassagneux, Dan Crisan and François Delarue The Annals of Applied Probability 29(3) (2019) https://doi.org/10.1214/18-AAP1429
Optimal Stabilization Control for Discrete-Time Mean-Field Stochastic Systems
Probabilistic Theory of Mean Field Games with Applications II
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Probabilistic Theory of Mean Field Games with Applications I
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Mean Field Games with Singular Controls of Bounded Velocity