Mean-Field Limit for a Class of Stochastic Ergodic Control Problems

DOI10.1137/20M1363479zbMath1483.49052arXiv2003.06469OpenAlexW3012550138WikidataQ114074157 ScholiaQ114074157MaRDI QIDQ5037500

Stefania Ugolini, Francesco C. De Vecchi, Andrea Romano, Sergio A. Albeverio

Publication date: 1 March 2022

Published in: SIAM Journal on Control and Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2003.06469

zbMATH Keywords

de Finetti's theoremmean-field controlMcKean-Vlasov limitergodic optimal controlconvergence of probability measures on path spacestrong Kac's chaos

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Strong limit theorems (60F15) Linear-quadratic optimal control problems (49N10) Linear optimal control problems (49N05) Mean field games and control (49N80)

Related Items (3)

Infinite-dimensional stochastic transforms and reproducing kernel Hilbert space ⋮ Some Connections Between Stochastic Mechanics, Optimal Control, and Nonlinear Schrödinger Equations ⋮ McKean Feynman-Kac probabilistic representations of non-linear partial differential equations

Cites Work

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• On the relation between optimal transport and Schrödinger bridges: a stochastic control viewpoint
• A weak approach to the stochastic deformation of classical mechanics
• A generalization of the Hopf-Cole transformation for stationary mean-field games systems
• Nonlinear elliptic systems and mean-field games
• On solutions of mean field games with ergodic cost
• The mathematics of the Bose gas and its condensation.
• Stochastic description of a Bose-Einstein condensate
• Second order mean field games with degenerate diffusion and local coupling
• Mean field games. I: The stationary case
• Forward-backward stochastic differential equations and controlled McKean-Vlasov dynamics
• Elliptic partial differential equations of second order
• An example of multiple mean field limits in ergodic differential games
• Mean-field games and swarms dynamics in Gaussian and non-Gaussian environments
• The mean field Schrödinger problem: ergodic behavior, entropy estimates and functional inequalities
• The master equation in mean field theory
• Entropy chaos and Bose-Einstein condensation
• A weak martingale approach to linear-quadratic Mckean-Vlasov stochastic control problems
• On Kac's chaos and related problems
• The derivation of ergodic mean field game equations for several populations of players
• Long Time Average of Mean Field Games with a Nonlocal Coupling
• Ergodic Control of Diffusion Processes
• Bellman equation and viscosity solutions for mean-field stochastic control problem
• Fokker–Planck–Kolmogorov Equations
• Pointwise Bounds on Eigenfunctions and Wave Packets in N-Body Quantum Systems. III
• Function Spaces with Exponential Weights I
• The Master Equation and the Convergence Problem in Mean Field Games
• Randomized dynamic programming principle and Feynman-Kac representation for optimal control of McKean-Vlasov dynamics
• Ergodicity for Infinite Dimensional Systems
• Strong Kac’s chaos in the mean-field Bose–Einstein Condensation
• Limit Theory for Controlled McKean--Vlasov Dynamics
• Probabilistic Theory of Mean Field Games with Applications I
• Probabilistic Theory of Mean Field Games with Applications II
• Envelope Theorems for Arbitrary Choice Sets
• Probabilistic Symmetries and Invariance Principles
• Dynamic Programming for Optimal Control of Stochastic McKean--Vlasov Dynamics
• Optimal Transport
• The kinetic and interaction energies of a trapped Bose gas: beyond the mean field

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