EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 31 (2025) ESAIM: COCV, 31 (2025) 6 References
Open Access
Issue
ESAIM: COCV
Volume 31, 2025
Article Number 6
Number of page(s) 38
DOI https://doi.org/10.1051/cocv/2024080
Published online 06 January 2025
  1. F. Cordoni and L. Di Persio, Optimal control for the stochastic Fitzhugh–Nagumo model with recovery variable. Evol. Eq. Control Theory 7 (2018) 571–585. [CrossRef] [Google Scholar]
  2. K. Du and Q. Meng, A maximum principle for optimal control of stochastic evolution equations. SIAM J. Control Optim. 51 (2013) 4343–4362. [Google Scholar]
  3. G. Fabbri, F. Gozzi and A. Świech, Stochastic Optimal Control in Infinite Dimension. Springer (2017). [CrossRef] [Google Scholar]
  4. H. Frankowska and X. Zhang, Necessary conditions for stochastic optimal control problems in infinite dimensions. Stochast. Process. Appl. 130 (2020) 4081–4103. [CrossRef] [Google Scholar]
  5. M. Fuhrman and C. Orrieri, Stochastic maximum principle for optimal control of a class of nonlinear SPDEs with dissipative drift. SIAM J. Control Optim. 54 (2016) 341–371. [Google Scholar]
  6. M. Fuhrman, Y. Hu and G. Tessitore, Stochastic maximum principle for optimal control of partial differential equations driven by white noise. Stoch. Part. Differ. Equ. Anal. Comput. 6 (2018) 255–285. [Google Scholar]
  7. Q. Lü and X. Zhang, General Pontryagin-Type Stochastic Maximum Principle and Backward Stochastic Evolution Equations in Infinite Dimensions. Springer (2014). [Google Scholar]
  8. Q. Lü and X. Zhang, Operator-valued backward stochastic Lyapunov equations in infinite dimensions, and its application. Math. Control Relat. Fields 8 (2018) 337–381. [CrossRef] [MathSciNet] [Google Scholar]
  9. W. Stannat and L. Wessels, Deterministic control of stochastic reaction-diffusion equations. Evol. Equ. Control Theory 10 (2021) 701–722. [CrossRef] [MathSciNet] [Google Scholar]
  10. W. Stannat and L. Wessels, Peng’s maximum principle for stochastic partial differential equations. SIAM J. Control Optim. 59 (2021) 3552–3573. [CrossRef] [MathSciNet] [Google Scholar]
  11. W. Stannat and L. Wessels, Necessary and sufficient conditions for optimal control of semilinear stochastic partial differential equations. arXiv:2112.09639 (2021). [Google Scholar]
  12. C. Beck, W.E. Jentzen and A. Jentzen, Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations. J. Nonlin. Sci. 29 (2019) 1563–1619. [CrossRef] [Google Scholar]
  13. R. Carmona and M. Laurière, Convergence analysis of machine learning algorithms for the numerical solution of mean field control and games. II. The finite horizon case. Ann. Appl. Probab. 32 (2022) 4065–4105. [CrossRef] [MathSciNet] [Google Scholar]
  14. S. Dolgov, D. Kalise and K.K. Kunisch, Tensor decomposition methods for high-dimensional Hamilton–Jacobi–Bellman equations. SIAM J. Sci. Comput. 43 (2021) A1625–A1650. [CrossRef] [Google Scholar]
  15. T. Dunst, A.K. Majee, A. Prohl and G. Vallet, On stochastic optimal control in ferromagnetism. Arch. Ration. Mech. Anal. 233 (2019) 1383–1440. [CrossRef] [MathSciNet] [Google Scholar]
  16. W.E.J. Han and A. Jentzen, Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations. Commun. Math. Stat. 5 (2017) 349–380. [CrossRef] [MathSciNet] [Google Scholar]
  17. A. Gorodetsky, S. Karaman and Y. Marzouk, High-dimensional stochastic optimal control using continuous tensor decompositions. Int. J. Robot. Res. 37 (2018) 340–377. [CrossRef] [Google Scholar]
  18. D. Kalise and K. Kunisch, Polynomial approximation of high-dimensional Hamilton–Jacobi–Bellman equations and applications to feedback control of semilinear parabolic PDEs. SIAM J. Sci. Comput. 40 (2018) A629–A652. [CrossRef] [Google Scholar]
  19. N. Nüsken and L. Richter, Solving high-dimensional Hamilton–Jacobi–Bellman PDEs using neural networks: perspectives from the theory of controlled diffusions and measures on path space. Part. Differ. Equ. Appl. 2 (2021) 1–48. [CrossRef] [Google Scholar]
  20. M. Oster, L. Sallandt and R. Schneider, Approximating optimal feedback controllers of finite horizon control problems using hierarchical tensor formats. SIAM J. Sci. Comput. 44 (2022) B746–B770. [CrossRef] [Google Scholar]
  21. R. Carmona and M. Laurière, Convergence analysis of machine learning algorithms for the numerical solution of mean field control and games. I. The ergodic case. SIAM J. Numer. Anal. 59 (2021) 1455–1485. [CrossRef] [MathSciNet] [Google Scholar]
  22. W. Stannat, A. Vogler and L. Wessels, Neural network approximation of optimal controls for stochastic reaction-diffusion equations. Chaos 33 (2023) 093118. [CrossRef] [PubMed] [Google Scholar]
  23. R. Kruse, Optimal error estimates of galerkin finite element methods for stochastic partial differential equations with multiplicative noise. IMA J. Numer. Anal. 34 (2014) 217–251. [CrossRef] [MathSciNet] [Google Scholar]
  24. W. Liu and M. Röckner, Stochastic Partial Differential Equations: An Introduction. Springer (2015). [CrossRef] [Google Scholar]
  25. C. Tudor, Quadratic control for stochastic systems defined by evolution operators and square integrable martingales. Math. Nachr. 147 (1990) 205–218. [CrossRef] [MathSciNet] [Google Scholar]
  26. A. Prohl and Y. Wang, Strong rates of convergence for a space-time discretization of the backward stochastic heat equation, and of a linear-quadratic control problem for the stochastic heat equation. ESAIM: COCV 27 (2021) 54. [CrossRef] [EDP Sciences] [Google Scholar]
  27. F. Flandoli and D. Gatarek, Martingale and stationary solutions for stochastic Navier–Stokes equations. Probab. Theory Relat. Fields. 102 (1995) 367–391. [CrossRef] [Google Scholar]
  28. M. Röckner, S. Shang and T. Zhang, Well-posedness of stochastic partial differential equations with fully local monotone coefficients. arXiv:2206.01107 (2022). [Google Scholar]
  29. J. Cui and J. Hong, Strong and weak convergence rates of a spatial approximation for stochastic partial differential equation with one-sided lipschitz coefficient. SIAM J. Num. Anal. 57 (2019) 1815–1841. [CrossRef] [Google Scholar]
  30. R. Carmona and F. Delarue, Probabilistic Theory of Mean Field Games with Applications II. Springer (2018). [Google Scholar]
  31. E. Pardoux, Stochastic Partial Differential Equations: An Introduction. Springer (2021). [CrossRef] [Google Scholar]
  32. A. Pinkus, Approximation theory of the mlp model in neural networks. Acta Numer. 8 (1999) 143–195. [CrossRef] [Google Scholar]
  33. H. Wendland, Scattered Data Approximation. Cambridge Monographs on Applied and Computational Mathematics. Cambridge University Press (2004). [CrossRef] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.