Open Access
Issue
ESAIM: COCV
Volume 30, 2024
Article Number 20
Number of page(s) 27
DOI https://doi.org/10.1051/cocv/2024012
Published online 07 March 2024
  1. H.J. Kushner, Necessary conditions for continuous parameter stochastic optimization problems. SIAM J. Control 10 (1972) 550–565. [CrossRef] [MathSciNet] [Google Scholar]
  2. J.-M. Bismut, Conjugate convex functions in optimal stochastic control. J. Math. Anal. Appl. 44 (1973) 384–404. [CrossRef] [MathSciNet] [Google Scholar]
  3. E. Pardoux and S. Peng, Adapted solution of a backward stochastic differential equation. Syst. Control Lett. 14 (1990) 55–61. [CrossRef] [Google Scholar]
  4. E. Pardoux and S. Peng, Backward doubly stochastic differential equations and systems of quasilinear spdes. Probab. Theory Related Fields 98 (1994) 209–227. [CrossRef] [MathSciNet] [Google Scholar]
  5. J. Yong and X.Y. Zhou, Stochastic controls: Hamiltonian systems and HJB equations. Vol. 43 of Applications of Mathematics (New York). Springer-Verlag, New York (1999) xxii+438. [Google Scholar]
  6. J. Zhang, Backward stochastic differential equations, in Backward Stochastic Differential Equations. Springer (2017) 79–99. [CrossRef] [Google Scholar]
  7. M. Kac, Foundations of kinetic theory, in Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, 1954–1955, Vol. III. University of California Press, Berkeley-Los Angeles, Calif. (1956) 171–197. [Google Scholar]
  8. A.-S. Sznitman, Topics in propagation of chaos, in Ecole d’été de probabilités de Saint-Flour XIX—1989. Springer (1991) 165–251. [Google Scholar]
  9. R. Buckdahn, B. Djehiche J. Li and S. Peng, Mean-field backward stochastic differential equations: a limit approach. Ann. Probab. 37 (2009) 1524–1565. [CrossRef] [MathSciNet] [Google Scholar]
  10. J. Li and C. Xing, General mean-field bdsdes with continuous coefficients. J. Math. Anal. Appl. 506 (2022) 125699. [CrossRef] [Google Scholar]
  11. J.-M. Lasry and P.-L. Lions, Mean field games. Jpn. J. Math. 2 (2007) 229–260. [Google Scholar]
  12. M. Huang, R.P. Malhamé and P.E. Caines, Large population stochastic dynamic games: closed-loop McKean–Vlasov systems and the Nash certainty equivalence principle. Commun. Inf. Syst. 6 (2006) 221–251. [CrossRef] [MathSciNet] [Google Scholar]
  13. R. Carmona and F. Delarue, Probabilistic analysis of mean-field games. SIAM J. Control Optim. 51 (2013) 2705–2734. [CrossRef] [MathSciNet] [Google Scholar]
  14. R. Carmona and F. Delarue, Forward–backward stochastic differential equations and controlled McKean–Vlasov dynamics. Ann. Probab. 43 (2015) 2647–2700. [CrossRef] [MathSciNet] [Google Scholar]
  15. R. Carmona and F. Delarue, Probabilistic theory of mean field games with applications. I. Vol. 83 of Probability Theory and Stochastic Modelling. Springer, Cham (2018) xxv+713. [Google Scholar]
  16. R. Buckdahn, B. Djehiche, and J. Li, A general stochastic maximum principle for SDEs of meanfield type. Appl. Math. Optim. 64 (2011) 197–216. [CrossRef] [MathSciNet] [Google Scholar]
  17. D. Andersson and B. Djehiche, A maximum principle for SDEs of mean-field type. Appl. Math. Optim. 63 (2011) 341–356. [Google Scholar]
  18. P.L. Lions, Théorie des jeux à champs moyen et applications. lectures at the collège de france, 2007–2008. [Google Scholar]
  19. P. Cardaliaguet, Notes from P. L. lions’ lectures at the collège de france, 2012. [Google Scholar]
  20. B. Acciaio, J. Backhoff-Veraguas and René Carmona, Extended mean field control problems: stochastic maximum principle and transport perspective. SIAM J. Control Optim. 57 (2019) 3666–3693. [CrossRef] [MathSciNet] [Google Scholar]
  21. R. Buckdahn, J. Li and J. Ma, A stochastic maximum principle for general mean-field systems. Appl. Math. Optim. 74 (2016) 507–534. [Google Scholar]
  22. T. Hao and Q. Meng, A global maximum principle for optimal control of general mean-field Forward–backward stochastic systems with jumps. ESAIM Control Optim. Calc. Var. 26 (2020) 39. [CrossRef] [EDP Sciences] [Google Scholar]
  23. R. Li and B. Liu, A maximum principle for fully coupled stochastic control systems of mean-field type. J. Math. Anal. Appl. 415 (2014) 902–930. [CrossRef] [MathSciNet] [Google Scholar]
  24. T. Nie and K. Yan, Extended mean-field control problem with partial observation. ESAIM Control Optim. Calc. Var. 28 (2022) 43. [CrossRef] [EDP Sciences] [Google Scholar]
  25. Y. Han, S. Peng and Z. Wu, Maximum principle for backward doubly stochastic control systems with applications. SIAM J. Control Optim. 48 (2010) 4224–4241. [CrossRef] [MathSciNet] [Google Scholar]
  26. L. Zhang and Y. Shi, Maximum principle for forward-backward doubly stochastic control systems and applications. ESAIM Control Optim. Calc. Var. 17 (2011) 1174–1197. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  27. L. Zhang, Q. Zhou and J. Yang, Necessary condition for optimal control of doubly stochastic systems. Math. Control Relat. Fields 10 (2020) 379–403. [Google Scholar]
  28. S. Peng and Y. Shi, A type of time-symmetric forward-backward stochastic differential equations. C. R. Math. Acad. Sci. Paris 336 (2003) 773–778. [CrossRef] [MathSciNet] [Google Scholar]
  29. S. Peng and Z. Wu, Fully coupled forward-backward stochastic differential equations and applications to optimal control. SIAM J. Control Optim. 37 (1999) 825–843. [CrossRef] [MathSciNet] [Google Scholar]
  30. Y. Hu and S. Peng, Solution of forward–backward stochastic differential equations. Probab. Theory Related Fields 103 (1995) 273–283. [CrossRef] [MathSciNet] [Google Scholar]
  31. A. Bensoussan, S.C. Phillip Yam and Z. Zhang, Well-posedness of mean-field type forward-backward stochastic differential equations. Stochastic Process. Appl. 125 (2015) 3327–3354. [CrossRef] [MathSciNet] [Google Scholar]

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