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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, 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

Stochastic Processes and their Applications, ISSN 0304-4149, 04/2020, Volume 130, Issue 4, pp. 2519 - 2551

We propose a particle system of diffusion processes coupled through a chain-like network structure described by an infinite-dimensional, nonlinear stochastic...

Detecting mean-field | Interacting stochastic processes | Stochastic equation with constraints | Particle system approximation | Law of large numbers | STATISTICS & PROBABILITY | PROPAGATION

Detecting mean-field | Interacting stochastic processes | Stochastic equation with constraints | Particle system approximation | Law of large numbers | STATISTICS & PROBABILITY | PROPAGATION

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

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

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

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

Journal Article

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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

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

Annals of Probability, ISSN 0091-1798, 03/2017, Volume 45, Issue 2, pp. 824 - 878

In this paper we consider a mean-field stochastic differential equation, also called Mc Kean-Vlasov equation, with initial data (t,x)is an element...

PDE of mean-field type | Value function | Mean-field stochastic differential equation | McKean-Vlasov equation | CHAOS | DYNAMICS | value function | STATISTICS & PROBABILITY | MCKEAN-VLASOV | LIMIT | PROPAGATION

PDE of mean-field type | Value function | Mean-field stochastic differential equation | McKean-Vlasov equation | CHAOS | DYNAMICS | value function | STATISTICS & PROBABILITY | MCKEAN-VLASOV | LIMIT | PROPAGATION

Journal Article

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Leader–follower stochastic differential game with asymmetric information and applications

Automatica, ISSN 0005-1098, 01/2016, Volume 63, pp. 60 - 73

This paper is concerned with a leader–follower stochastic differential game with asymmetric information, where the information available to the follower is...

Asymmetric information | Leader–follower stochastic differential game | Filtering | Partial information linear–quadratic control | Conditional mean-field forward–backward stochastic differential equation | Open-loop Stackelberg equilibrium | Partial information linear-quadratic control | Conditional mean-field forward-backward stochastic differential equation | Leader-follower stochastic differential game | MAXIMUM PRINCIPLE | EQUATIONS | AUTOMATION & CONTROL SYSTEMS | STRATEGIES | ENGINEERING, ELECTRICAL & ELECTRONIC | Algebra

Asymmetric information | Leader–follower stochastic differential game | Filtering | Partial information linear–quadratic control | Conditional mean-field forward–backward stochastic differential equation | Open-loop Stackelberg equilibrium | Partial information linear-quadratic control | Conditional mean-field forward-backward stochastic differential equation | Leader-follower stochastic differential game | MAXIMUM PRINCIPLE | EQUATIONS | AUTOMATION & CONTROL SYSTEMS | STRATEGIES | ENGINEERING, ELECTRICAL & ELECTRONIC | Algebra

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 10/2019, Volume 187, pp. 259 - 278

The existence and uniqueness of measure-valued solutions to stochastic nonlinear, non-local Fokker–Planck equations is proven. This type of stochastic PDE is...

Stochastic Fokker–Planck equations | Particle representations | McKean–Vlasov equations | MATHEMATICS | MATHEMATICS, APPLIED | McKean-Vlasov equations | PARTIAL-DIFFERENTIAL-EQUATIONS | SCALAR CONSERVATION-LAWS | MEAN-FIELD GAMES | Stochastic Fokker-Planck equations | PROPAGATION | UNIQUENESS | Mathematical analysis | Nonlinear equations | Uniqueness

Stochastic Fokker–Planck equations | Particle representations | McKean–Vlasov equations | MATHEMATICS | MATHEMATICS, APPLIED | McKean-Vlasov equations | PARTIAL-DIFFERENTIAL-EQUATIONS | SCALAR CONSERVATION-LAWS | MEAN-FIELD GAMES | Stochastic Fokker-Planck equations | PROPAGATION | UNIQUENESS | Mathematical analysis | Nonlinear equations | Uniqueness

Journal Article

Asian Journal of Control, ISSN 1561-8625, 03/2019, Volume 21, Issue 2, pp. 809 - 823

In this paper, we study a linear‐quadratic optimal control problem for mean‐field stochastic differential equations driven by a Poisson random martingale...

Mean‐field | optimal control | adjoint processes | feedback representation | Mean-field | Differential equations | College teachers

Mean‐field | optimal control | adjoint processes | feedback representation | Mean-field | Differential equations | College teachers

Journal Article

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Strong well posedness of McKean–Vlasov stochastic differential equations with Hölder drift

Stochastic Processes and their Applications, ISSN 0304-4149, 01/2020, Volume 130, Issue 1, pp. 79 - 107

Here, we prove strong well-posedness for stochastic systems of McKean–Vlasov type with Hölder drift, even in the measure argument, and uniformly non-degenerate...

McKean–Vlasov processes | Smoothing effect | Non-linear PDE | Regularization by noise | STATISTICS & PROBABILITY | MEAN-FIELD GAMES | McKean-Vlasov processes

McKean–Vlasov processes | Smoothing effect | Non-linear PDE | Regularization by noise | STATISTICS & PROBABILITY | MEAN-FIELD GAMES | McKean-Vlasov processes

Journal Article

STOCHASTICS AND DYNAMICS, ISSN 0219-4937, 02/2020, Volume 20, Issue 1

We consider McKean-Vlasov stochastic differential equations (MVSDEs), which are SDEs where the drift and diffusion coefficients depend not only on the state of...

martingale measure | mean-field control | Wasserstein metric | existence | STATISTICS & PROBABILITY | McKean-Vlasov stochastic differential equation | stability | relaxed control

martingale measure | mean-field control | Wasserstein metric | existence | STATISTICS & PROBABILITY | McKean-Vlasov stochastic differential equation | stability | relaxed control

Journal Article

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Stochastic Control for Mean-Field Stochastic Partial Differential Equations with Jumps

Journal of Optimization Theory and Applications, ISSN 0022-3239, 3/2018, Volume 176, Issue 3, pp. 559 - 584

We study optimal control for mean-field stochastic partial differential equations (stochastic evolution equations) driven by a Brownian motion and an...

Mean-field backward stochastic partial differential equation | 35R60 | Mathematics | Theory of Computation | Mean-field stochastic partial differential equation | Optimization | 93E20 | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Optimal control | Stochastic maximum principles | Applications of Mathematics | Engineering, general | 60H15 | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Harvesting | Differential equations | Partial differential equations | Mathematical analysis | Stochastic processes | Maximum principle | Brownian movements

Mean-field backward stochastic partial differential equation | 35R60 | Mathematics | Theory of Computation | Mean-field stochastic partial differential equation | Optimization | 93E20 | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Optimal control | Stochastic maximum principles | Applications of Mathematics | Engineering, general | 60H15 | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Harvesting | Differential equations | Partial differential equations | Mathematical analysis | Stochastic processes | Maximum principle | Brownian movements

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 10/2015, Volume 299, pp. 429 - 445

Reaction–diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such...

Stochastic model | Reaction–diffusion system | Lotka–Volterra equation | Hybrid model | Fisher–Kolmogorov equation | Reaction-diffusion system | Fisher-Kolmogorov equation | Lotka-Volterra equation | ALGORITHM REFINEMENT | COUPLED CHEMICAL-REACTIONS | NOISE | TIME | SIMULATION | PHYSICS, MATHEMATICAL | INVASION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | PARTIAL-DIFFERENTIAL-EQUATIONS | DYNAMICS | SYSTEMS | PROPAGATION | Analysis | Models | Biomedical engineering | Computer simulation | Partial differential equations | Preserves | Lattice sites | Bacteria | Ecology | Mathematical models | Stochasticity | FOKKER-PLANCK EQUATION | BACTERIA | DIFFUSION EQUATIONS | ERRORS | STOCHASTIC PROCESSES | PARTICLES | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | VOLTERRA INTEGRAL EQUATIONS | COMPUTERIZED SIMULATION | MOLECULES | CHAPMAN-KOLMOGOROV EQUATION | DETERMINISTIC ESTIMATION | MEAN-FIELD THEORY | ATOMS

Stochastic model | Reaction–diffusion system | Lotka–Volterra equation | Hybrid model | Fisher–Kolmogorov equation | Reaction-diffusion system | Fisher-Kolmogorov equation | Lotka-Volterra equation | ALGORITHM REFINEMENT | COUPLED CHEMICAL-REACTIONS | NOISE | TIME | SIMULATION | PHYSICS, MATHEMATICAL | INVASION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | PARTIAL-DIFFERENTIAL-EQUATIONS | DYNAMICS | SYSTEMS | PROPAGATION | Analysis | Models | Biomedical engineering | Computer simulation | Partial differential equations | Preserves | Lattice sites | Bacteria | Ecology | Mathematical models | Stochasticity | FOKKER-PLANCK EQUATION | BACTERIA | DIFFUSION EQUATIONS | ERRORS | STOCHASTIC PROCESSES | PARTICLES | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | VOLTERRA INTEGRAL EQUATIONS | COMPUTERIZED SIMULATION | MOLECULES | CHAPMAN-KOLMOGOROV EQUATION | DETERMINISTIC ESTIMATION | MEAN-FIELD THEORY | ATOMS

Journal Article

Asian Journal of Control, ISSN 1561-8625, 11/2017, Volume 19, Issue 6, pp. 2097 - 2115

This paper deals with the risk‐sensitive control problem for mean‐field stochastic delay differential equations (MF‐SDDEs) with partial information. Firstly,...

risk‐sensitive control | stochastic delay differential equations | Stochastic maximum principle | mean‐field type | continuous dependence theorem | risk-sensitive control | mean-field type | MAXIMUM PRINCIPLE | SYSTEMS | AUTOMATION & CONTROL SYSTEMS | Differential equations

risk‐sensitive control | stochastic delay differential equations | Stochastic maximum principle | mean‐field type | continuous dependence theorem | risk-sensitive control | mean-field type | MAXIMUM PRINCIPLE | SYSTEMS | AUTOMATION & CONTROL SYSTEMS | Differential equations

Journal Article

Electronic Communications in Probability, ISSN 1083-589X, 2013, Volume 18, pp. 1 - 15

The purpose of this note is to provide an existence result for the solution of fully coupled Forward Backward Stochastic Differential Equations (FBSDEs) of the...

FBSDEs | Mean field interactions | EXISTENCE | STATISTICS & PROBABILITY | Mean Field Interactions | UNIQUENESS | Probability | Mathematics

FBSDEs | Mean field interactions | EXISTENCE | STATISTICS & PROBABILITY | Mean Field Interactions | UNIQUENESS | Probability | Mathematics

Journal Article

European Journal of Control, ISSN 0947-3580, 07/2017, Volume 36, pp. 43 - 50

This paper investigates an optimal control of an infinite horizon system governed by mean-field backward stochastic differential equation with delay and...

Partial information | Infinite horizon | Backward stochastic differential delay equation | Stochastic maximum principle | Mean-field model | MAXIMUM PRINCIPLE | SYSTEMS | AUTOMATION & CONTROL SYSTEMS | Control systems | Stochastic differential equations | Research | Mathematical optimization | Stochastic control theory | Economic models | Filtration | Partial differential equations | Probability theory | Uniqueness | Delay | Control | Mathematical analysis | Optimal control | Differential equations | Inventory management | Portfolio management | Inequality

Partial information | Infinite horizon | Backward stochastic differential delay equation | Stochastic maximum principle | Mean-field model | MAXIMUM PRINCIPLE | SYSTEMS | AUTOMATION & CONTROL SYSTEMS | Control systems | Stochastic differential equations | Research | Mathematical optimization | Stochastic control theory | Economic models | Filtration | Partial differential equations | Probability theory | Uniqueness | Delay | Control | Mathematical analysis | Optimal control | Differential equations | Inventory management | Portfolio management | Inequality

Journal Article

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