Mean-field backward stochastic differential equations: A limit approach

Annals of Probability

Volumn 37, Issue 4, 2009, Pages 1524-1565

  Buckdahn, Rainer ^a   Djehiche, Boualem ^b   Li, Juan ^c   Peng, Shige ^d  

^a UNIVERSITÉ DE BRETAGNE OCCIDENTALE   (France)

^b ROYAL INSTITUTE OF TECHNOLOGY   (Sweden)

^c SHANDONG UNIVERSITY   (China)

^d SHANDONG UNIVERSITY   (China)

Author keywords

Backward stochastic differential equation; McKean Vlasov equation; Mean field approach; Mean field BSDE; Tightness; Weak convergence

Indexed keywords

EID: 69249229620     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/08-AOP442     Document Type: Article

References (17)

1. Bossy, M. (2005). Some stochastic particle methods for nonlinear parabolic PDEs. In GRIP-Research Group on Particle Interactions. ESAIM Proceedings 15 18-57. MR2441320
2. Bossy, M. and TALAY, D. (1997). A stochastic particle method for the McKean-Vlasov and the Burgers equation. Math. Comp. 66 157-192. MR1370849
3. Buckdahn, R., LI, J. and Peng, S. (2007).Mean-field backward stochastic differential equations and related patial differential equations. Submitted. Available at http://arxiv.org/abs/0711.2167.
4. Chan, T. (1994). Dynamics of the McKean-Vlasov equation. Ann. Probab. 22 431-441. MR1258884
5. El Karoui, N., Peng, S. And quenez, M. C. (1997). Backward stochastic differential equations in finance. Math. Finance 7 1-71. MR1434407
6. Kotelenez, P. (1995). A class of quasilinear stochastic partial differential equations of McKean-Vlasov type with mass conservation. Probab. Theory Related Fields 102 159-188. MR1337250
7. Lasry, J.-M. and Lions, P.-L. (2007). Mean field games. Japan J. Math. 2 229-260. MR2295621
8. Méléard, S. (1996). Asymptotic behaviour of some interacting particle systems; McKean-Vlasov and Boltzmann models. In Probabilistic Models for Nonlinear Partial Differential Equations (Montecatini Terme, 1995). Lecture Notes in Math. 1627 42-95. Springer, Berlin. MR1431299
9. Nualart, D. (1995). The Malliavin Calculus and Related Topics. Springer, New York. MR1344217
10. Overbeck, L. (1995). Superprocesses and McKean-Vlasov equations with creation of mass. Preprint.
11. Pardoux, É. and Peng, S. G. (1990). Adapted solution of a backward stochastic differential equation. Systems Control Lett. 14 61-74. MR1037747
12. Pardoux, É. and Peng, S. (1992). Backward stochastic differential equations and quasilinear parabolic partial differential equations. In Stochastic Partial Differential Equations and Their Applications (Charlotte, NC, 1991). Lecture Notes in Control and Information Sciences 176 200-217. Springer, Berlin. MR1176785
13. Peng, S. G. (1992). A generalized dynamic programming principle and Hamilton-Jacobi-Bellman equation. Stochastics Rep. 38 119-134. MR1274898
14. Pra, P. D. and Hollander, F. D. (1995). McKean-Vlasov limit for interacting random processes in random media. J. Statist. Phys. 84 735-772. MR1400186
15. Sznitman, A.-S. (1984). Nonlinear reflecting diffusion process, and the propagation of chaos and fluctuations associated. J. Funct. Anal. 56 311-336. MR743844
16. Sznitman, A.-S. (1991). Topics in propagation of chaos. In École D'Été de Probabilités de Saint-Flour XIX-1989. Lecture Notes in Math. 1464 165-252. Springer, Berlin. MR1108185
17. Talay, D. and Vaillant, O. (2003). A stochastic particle method with random weights for the computation of statistical solutions of McKean-Vlasov equations. Ann. Appl. Probab. 13 140-180. MR1951996