Mean field forward-backward stochastic differential equations

Electronic Communications in Probability

Volumn 18, Issue , 2013, Pages

  Carmon, René ^a   Delarue, Francois ^b  

^a PRINCETON UNIVERSITY   (United States)

^b UNIVERSITÉ DE NICE SOPHIA ANTIPOLIS   (France)

Author keywords

FBSDEs; Mean field interactions

Indexed keywords

EID: 84881285990     PISSN: None     EISSN: 1083589X     Source Type: Journal    
DOI: 10.1214/ECP.v18-2446     Document Type: Article

References (18)

1. A. Bensoussan, K.C.J. Sung, S.C.P. Yam, and S.P. Yung. Linear quadratic mean field games. Technical report, 2011.
2. P. Cardaliaguet. Notes on mean field games. Technical report, 2010.
3. R. Carmona and F. Delarue. Optimal control of McKean-Vlasov stochastic dynamics. Technical report, 2012. arXiv:1211.4186
4. R. Carmona and F. Delarue. Probabilistic analysis of mean field games. SIAM Journal on Control and Optimization, 51:2705-2734, 2013. MR-3072222
5. R. Carmona, F. Delarue, and A. Lachapelle. Control of McKean-Vlasov versus Mean Field Games. Mathematics and Financial Economics, 7:131-166, 2013. MR-3045029
6. F. Delarue. On the existence and uniqueness of solutions to FBSDEs in a non-degeneratecase. Stochastic Processes and Applications, 99:209-286, 2002. MR-1901154
7. F. Delarue. Estimates of the solutions of a system of quasi-linear PDEs. a probabilistic scheme. Séminaire de Probabilités XXXVII, pages 290-332. Springer Verlag, 2003. MR-2053051
8. F. Delarue and G. Guatteri. Weak existence and uniqueness for fbsdes. Stochastic Processes and Applications, 116:1712-1742, 2006. MR-2307056
9. Avner Friedman. Partial differential equations of parabolic type. Prentice-Hall, Englewood Cliffs, N.J., first edition, 1964. MR-0181836
10. B. Jourdain, S. Meleard, and W. Woyczynski. Nonlinear SDEs driven by Lévy processes and related PDEs. ALEA, Latin American Journal of Probability, 4:1-29, 2008. MR-2383731
11. M. Kac. Foundations of kinetic theory. In Proceedings of the 3rd Berkeley Symposium on Mathematical Statistics and Probability, volume 3, pages 171-197, 1956. MR-0084985
12. M. Kac. Probability and Related Topics in the Physical Sciences. Interscience, 1958. MR-0102849
13. B. F. Knerr. Parabolic interior schauder estimates by the maximum principle. Archive for Rational Mechanics and Analysis.
14. J.M. Lasry and P.L.Lions. Jeux à champ moyen i. le cas stationnaire. Comptes Rendus de l'Académie des Sciences de Paris, ser. A, 343(9), 2006. MR-2269875
15. J.M. Lasry and P.L.Lions. Jeux à champ moyen ii. horizon fini et contrôle optimal. Comptes Rendus de l'Académie des Sciences de Paris, ser. A, 343(10), 2006. MR-2271747
16. J.M. Lasry and P.L.Lions. Mean field games. Japanese Journal of Mathematics, 2(1), Mar. 2007. MR-2295621
17. A.S. Sznitman. Topics in propagation of chaos. In D. L. Burkholder et al. Ecole de Prob-abilités de Saint Flour, XIX-1989, volume 1464 of Lecture Notes in Mathematics, pages 165-251, 1989. MR-1108185
18. J. Yong. A linear-quadratic optimal control problem for mean field stochastic differential equations. Technical report, 2011.