Automatica, ISSN 0005-1098, 12/2017, Volume 86, pp. 104 - 109

This article is concerned with an optimal control problem derived by mean-field forward–backward stochastic differential equation with noisy observation, where...

Mean-field forward–backward stochastic differential equation | Maximum principle | Recursive utility | Optimal filter | Backward separation method | INFINITE-HORIZON | GAMES | RISK | ENGINEERING, ELECTRICAL & ELECTRONIC | CONTROL SYSTEMS | FINANCE | MCKEAN-VLASOV DYNAMICS | AUTOMATION & CONTROL SYSTEMS | Mean-field forward-backward stochastic differential equation | Analysis | Differential equations

Mean-field forward–backward stochastic differential equation | Maximum principle | Recursive utility | Optimal filter | Backward separation method | INFINITE-HORIZON | GAMES | RISK | ENGINEERING, ELECTRICAL & ELECTRONIC | CONTROL SYSTEMS | FINANCE | MCKEAN-VLASOV DYNAMICS | AUTOMATION & CONTROL SYSTEMS | Mean-field forward-backward stochastic differential equation | Analysis | Differential equations

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

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

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Second relativistic mean field and virial equation of state for astrophysical simulations

Physical Review C - Nuclear Physics, ISSN 0556-2813, 06/2011, Volume 83, Issue 6

We generate a second equation of state (EOS) of nuclear matter for a wide range of temperatures, densities, and proton fractions for use in supernovae, neutron...

DENSITY | PHYSICS, NUCLEAR | SUPERNOVA | NUCLEAR-MATTER | THERMODYNAMIC PROPERTIES | NEUTRON STARS | ENERGY RANGE | EQUATIONS | FERMIONS | SUPERNOVAE | RELATIVISTIC RANGE | ASTROPHYSICS, COSMOLOGY AND ASTRONOMY | MEAN-FIELD THEORY | MASS | PHYSICAL PROPERTIES | EQUATIONS OF STATE | ERUPTIVE VARIABLE STARS | MEV RANGE | BINARY STARS | MATTER | VIRIAL EQUATION | INTERACTIONS | SIMULATION | PROTONS | ELEMENTARY PARTICLES | BLACK HOLES | NUCLEONS | NUCLEAR MATTER | NUCLEAR PHYSICS AND RADIATION PHYSICS | TEMPERATURE RANGE | VARIABLE STARS | ASTROPHYSICS | EXPANSION | STARS | PHYSICS | BARYONS | HADRONS

DENSITY | PHYSICS, NUCLEAR | SUPERNOVA | NUCLEAR-MATTER | THERMODYNAMIC PROPERTIES | NEUTRON STARS | ENERGY RANGE | EQUATIONS | FERMIONS | SUPERNOVAE | RELATIVISTIC RANGE | ASTROPHYSICS, COSMOLOGY AND ASTRONOMY | MEAN-FIELD THEORY | MASS | PHYSICAL PROPERTIES | EQUATIONS OF STATE | ERUPTIVE VARIABLE STARS | MEV RANGE | BINARY STARS | MATTER | VIRIAL EQUATION | INTERACTIONS | SIMULATION | PROTONS | ELEMENTARY PARTICLES | BLACK HOLES | NUCLEONS | NUCLEAR MATTER | NUCLEAR PHYSICS AND RADIATION PHYSICS | TEMPERATURE RANGE | VARIABLE STARS | ASTROPHYSICS | EXPANSION | STARS | PHYSICS | BARYONS | HADRONS

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

Hartree equation | Classical limit | Mean-field limit | Schrödinger equation | MATHEMATICS | Schrodinger equation | QUANTUM | DYNAMICS

Journal Article

The Annals of Probability, ISSN 0091-1798, 7/2009, Volume 37, Issue 4, pp. 1524 - 1565

Mathematical mean-field approaches play an important role in different fields of Physics and Chemistry, but have found in recent works also their application...

Brownian motion | Approximation | Constant coefficients | Uniqueness | Differential equations | Random variables | Coefficients | Probabilities | Perceptron convergence procedure | Mean-field BSDE | Weak convergence | Tightness | Backward stochastic differential equation | Mean-field approach | McKean-Vlasov equation | mean-field approach | tightness | STATISTICS & PROBABILITY | MCKEAN-VLASOV | weak convergence | mean-field BSDE | PARTICLE METHOD | 60H10 | 60B10 | McKean–Vlasov equation | particle method | mckean-vlasov

Brownian motion | Approximation | Constant coefficients | Uniqueness | Differential equations | Random variables | Coefficients | Probabilities | Perceptron convergence procedure | Mean-field BSDE | Weak convergence | Tightness | Backward stochastic differential equation | Mean-field approach | McKean-Vlasov equation | mean-field approach | tightness | STATISTICS & PROBABILITY | MCKEAN-VLASOV | weak convergence | mean-field BSDE | PARTICLE METHOD | 60H10 | 60B10 | McKean–Vlasov equation | particle method | mckean-vlasov

Journal Article

Archive for Rational Mechanics and Analysis, ISSN 0003-9527, 1/2017, Volume 223, Issue 1, pp. 57 - 94

In this paper, we establish (1) the classical limit of the Hartree equation leading to the Vlasov equation, (2) the classical limit of the N-body linear...

Physics, general | Fluid- and Aerodynamics | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | Classical Mechanics | MATHEMATICS, APPLIED | MECHANICS | APPROXIMATION | CLASSICAL LIMIT | QUANTUM | Classical mechanics | Liouville equations | Schroedinger equation | Mathematical analysis | Byproducts | Vlasov equations | Estimates | Density | Mathematics | Mathematical Physics | Analysis of PDEs

Physics, general | Fluid- and Aerodynamics | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | Classical Mechanics | MATHEMATICS, APPLIED | MECHANICS | APPROXIMATION | CLASSICAL LIMIT | QUANTUM | Classical mechanics | Liouville equations | Schroedinger equation | Mathematical analysis | Byproducts | Vlasov equations | Estimates | Density | Mathematics | Mathematical Physics | Analysis of PDEs

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

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

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

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

In [R. Buckdahn, B. Djehiche, J. Li, S. Peng, Mean-field backward stochastic differential equations. A limit approach. Ann. Probab. (2007) (in press)....

Dynamic programming principle | Backward stochastic differential equations | Mean-field models | Comparison theorem | McKean–Vlasov equation | Viscosity solution | McKean-Vlasov equation | VISCOSITY SOLUTIONS | GAMES | STATISTICS & PROBABILITY | MCKEAN-VLASOV | Mean-field models McKean-Vlasov equation Backward stochastic differential equations Comparison theorem Dynamic programming principle Viscosity solution | Markov processes | Analysis

Dynamic programming principle | Backward stochastic differential equations | Mean-field models | Comparison theorem | McKean–Vlasov equation | Viscosity solution | McKean-Vlasov equation | VISCOSITY SOLUTIONS | GAMES | STATISTICS & PROBABILITY | MCKEAN-VLASOV | Mean-field models McKean-Vlasov equation Backward stochastic differential equations Comparison theorem Dynamic programming principle Viscosity solution | Markov processes | Analysis

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The mean field kinetic equation for interacting particle systems with non‐Lipschitz force

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

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

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

Asian Journal of Control, ISSN 1561-8625, 2019

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

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

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Linear-quadratic optimal control problems for mean-field stochastic differential equations

SIAM Journal on Control and Optimization, ISSN 0363-0129, 2013, Volume 51, Issue 4, pp. 2809 - 2838

Linear-quadratic optimal control problems are considered for mean-field stochastic differential equations with deterministic coefficients. By a variational...

Feedback representation | Riccati differential equation | Mean-field stochastic differential equation | Linear-quadratic optimal control | MATHEMATICS, APPLIED | DIFFUSIONS | feedback representation | linear-quadratic optimal control | EVOLUTION EQUATION | DYNAMICS | mean-field stochastic differential equation | LIMIT | HILBERT-SPACE | MCKEAN-VLASOV EQUATION | AUTOMATION & CONTROL SYSTEMS | Decoupling | Variational methods | Optimal control | Differential equations | Control systems | Representations | Stochasticity | Optimization

Feedback representation | Riccati differential equation | Mean-field stochastic differential equation | Linear-quadratic optimal control | MATHEMATICS, APPLIED | DIFFUSIONS | feedback representation | linear-quadratic optimal control | EVOLUTION EQUATION | DYNAMICS | mean-field stochastic differential equation | LIMIT | HILBERT-SPACE | MCKEAN-VLASOV EQUATION | AUTOMATION & CONTROL SYSTEMS | Decoupling | Variational methods | Optimal control | Differential equations | Control systems | Representations | Stochasticity | Optimization

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

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

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FORWARD–BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS AND CONTROLLED MCKEAN–VLASOV DYNAMICS

The Annals of Probability, ISSN 0091-1798, 9/2015, Volume 43, Issue 5, pp. 2647 - 2700

The purpose of this paper is to provide a detailed probabilistic analysis of the optimal control of nonlinear stochastic dynamical systems of McKean–Vlasov...

Stochastic control | Stochastic Pontryagin principle | Mckean-Vlasov diffusion | Mean-field interaction | Mean-field forward-backward stochastic differential equation | stochastic Pontryagin principle | mean-field forward-backward stochastic differential equation | McKean-Vlasov diffusion | STATISTICS & PROBABILITY | MEAN-FIELD GAMES | mean-field interaction | Probability | Mathematics | 93E20 | 60H10 | McKean–Vlasov diffusion | 60K35 | mean-field forward–backward stochastic differential equation

Stochastic control | Stochastic Pontryagin principle | Mckean-Vlasov diffusion | Mean-field interaction | Mean-field forward-backward stochastic differential equation | stochastic Pontryagin principle | mean-field forward-backward stochastic differential equation | McKean-Vlasov diffusion | STATISTICS & PROBABILITY | MEAN-FIELD GAMES | mean-field interaction | Probability | Mathematics | 93E20 | 60H10 | McKean–Vlasov diffusion | 60K35 | mean-field forward–backward stochastic differential equation

Journal Article

Automatica, ISSN 0005-1098, 06/2014, Volume 50, Issue 6, pp. 1565 - 1579

This paper investigates a stochastic optimal control problem with delay and of mean-field type, where the controlled state process is governed by a mean-field...

Backward stochastic differential equation | Stochastic delay differential equation | Stochastic maximum principle | Mean–variance portfolio selection | Mean-field model | Mean-variance portfolio selection | SYSTEMS | MODEL | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Differential equations | Automation | Finance | Optimal control | Maximum principle | Stochasticity | Delay

Backward stochastic differential equation | Stochastic delay differential equation | Stochastic maximum principle | Mean–variance portfolio selection | Mean-field model | Mean-variance portfolio selection | SYSTEMS | MODEL | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Differential equations | Automation | Finance | Optimal control | Maximum principle | Stochasticity | Delay

Journal Article

Science, ISSN 0036-8075, 11/2002, Volume 298, Issue 5598, pp. 1592 - 1596

Nuclear collisions can compress nuclear matter to densities achieved within neutron stars and within core-collapse supernovae. These dense states of matter...

Protons | Reserarch Articles | Neutron stars | Equations of state | Flux density | Projectiles | Self consistent fields | Neutrons | Nucleons | Momentum | Density | PLUS AU COLLISIONS | COLLECTIVE FLOW | MEAN-FIELD THEORY | ELLIPTIC FLOW | MULTIDISCIPLINARY SCIENCES | HEAVY-ION COLLISIONS | NEUTRON-STARS | NUCLEAR-EQUATION | AU+AU COLLISIONS | OUT-OF-PLANE | MOMENTUM-DEPENDENT INTERACTIONS | Matter | Research | Analysis | Methods | Nuclear physics | Supernovae | Matter & antimatter | Astrophysics | Physics - Nuclear Theory

Protons | Reserarch Articles | Neutron stars | Equations of state | Flux density | Projectiles | Self consistent fields | Neutrons | Nucleons | Momentum | Density | PLUS AU COLLISIONS | COLLECTIVE FLOW | MEAN-FIELD THEORY | ELLIPTIC FLOW | MULTIDISCIPLINARY SCIENCES | HEAVY-ION COLLISIONS | NEUTRON-STARS | NUCLEAR-EQUATION | AU+AU COLLISIONS | OUT-OF-PLANE | MOMENTUM-DEPENDENT INTERACTIONS | Matter | Research | Analysis | Methods | Nuclear physics | Supernovae | Matter & antimatter | Astrophysics | Physics - Nuclear Theory

Journal Article