Optimal control of stochastic differential equations via Fokker-Planck equations

DOI10.1007/s00245-021-09804-5zbMath1485.93621OpenAlexW3186379569WikidataQ115388190 ScholiaQ115388190MaRDI QIDQ832606

Ştefana-Lucia Aniţa

Publication date: 25 March 2022

Published in: Applied Mathematics and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00245-021-09804-5

zbMATH Keywords

stochastic differential equationweak solutionFokker-Planck equationfeedback controlstochastic optimal control problemdeterministic optimal control problem

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Feedback control (93B52) Optimal stochastic control (93E20) Existence theories for optimal control problems involving partial differential equations (49J20) Weak solutions to PDEs (35D30) Fokker-Planck equations (35Q84)

Related Items (4)

Existence of Optimal Control for Nonlinear Fokker–Planck Equations in \(\boldsymbol{L^1(\mathbb{R}^d)}\). ⋮ Controlling a generalized Fokker-Planck equation via inputs with nonlocal action ⋮ Stochastic gradient descent with noise of machine learning type. II: Continuous time analysis ⋮ Optimal control for stochastic differential equations and related Kolmogorov equations

Cites Work

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• Well-posedness of multidimensional diffusion processes with weakly differentiable coefficients
• Stochastic differential equations with variable structure driven by multiplicative Gaussian noise and sliding mode dynamic
• Kolmogorov equations for stochastic PDEs.
• From nonlinear Fokker-Planck equations to solutions of distribution dependent SDE
• Weak uniqueness of Fokker-Planck equations with degenerate and bounded coefficients
• Generalized Fokker-Planck equation: derivation and exact solutions
• Optimal control of the Fokker-Planck equation with space-dependent controls
• Analysis and control of nonlinear infinite dimensional systems
• Feedback optimal controllers for the Heston model
• Fully decoupled, linear and unconditionally energy stable time discretization scheme for solving the magneto-hydrodynamic equations
• Existence and uniqueness of martingale solutions for SDEs with rough or degenerate coefficients
• Optimal control of conditioned processes with feedback controls
• Probabilistic Representation for Solutions to Nonlinear Fokker--Planck Equations
• The first variation and Pontryagin’s maximum principle in optimal control for partial differential equations
• User’s guide to viscosity solutions of second order partial differential equations
• Optimal Feedback Controllers for a Stochastic Differential Equation with Reflection
• Optimal Control of Nonlinear Stochastic Differential Equations on Hilbert Spaces
• Stochastic differential equations. An introduction with applications.

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