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 |
- H.J. Kushner, Necessary conditions for continuous parameter stochastic optimization problems. SIAM J. Control 10 (1972) 550–565. [CrossRef] [MathSciNet] [Google Scholar]
- J.-M. Bismut, Conjugate convex functions in optimal stochastic control. J. Math. Anal. Appl. 44 (1973) 384–404. [CrossRef] [MathSciNet] [Google Scholar]
- E. Pardoux and S. Peng, Adapted solution of a backward stochastic differential equation. Syst. Control Lett. 14 (1990) 55–61. [CrossRef] [Google Scholar]
- 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]
- 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]
- J. Zhang, Backward stochastic differential equations, in Backward Stochastic Differential Equations. Springer (2017) 79–99. [CrossRef] [Google Scholar]
- 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]
- 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]
- 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]
- J. Li and C. Xing, General mean-field bdsdes with continuous coefficients. J. Math. Anal. Appl. 506 (2022) 125699. [CrossRef] [Google Scholar]
- J.-M. Lasry and P.-L. Lions, Mean field games. Jpn. J. Math. 2 (2007) 229–260. [Google Scholar]
- 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]
- R. Carmona and F. Delarue, Probabilistic analysis of mean-field games. SIAM J. Control Optim. 51 (2013) 2705–2734. [CrossRef] [MathSciNet] [Google Scholar]
- 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]
- 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]
- 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]
- D. Andersson and B. Djehiche, A maximum principle for SDEs of mean-field type. Appl. Math. Optim. 63 (2011) 341–356. [Google Scholar]
- P.L. Lions, Théorie des jeux à champs moyen et applications. lectures at the collège de france, 2007–2008. [Google Scholar]
- P. Cardaliaguet, Notes from P. L. lions’ lectures at the collège de france, 2012. [Google Scholar]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- Y. Hu and S. Peng, Solution of forward–backward stochastic differential equations. Probab. Theory Related Fields 103 (1995) 273–283. [CrossRef] [MathSciNet] [Google Scholar]
- 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]
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.