Mean-field backward stochastic differential equations and related partial differential equations

Stochastic Processes and their Applications

Volumn 119, Issue 10, 2009, Pages 3133-3154

  Buckdahn, Rainer ^a   Li, Juan ^b   Peng, Shige ^c  

^a UNIVERSITÉ DE BRETAGNE OCCIDENTALE   (France)

^b SHANDONG UNIVERSITY   (China)

^c SHANDONG UNIVERSITY   (China)

Author keywords

Backward stochastic differential equations; Comparison theorem; Dynamic programming principle; McKean Vlasov equation; Mean field models; Viscosity solution

Indexed keywords

BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS; COMPARISON THEOREM; DYNAMIC PROGRAMMING PRINCIPLE; MCKEAN-VLASOV EQUATION; MEAN-FIELD MODELS; VISCOSITY SOLUTION;

AIRCRAFT ENGINES; COMPUTATIONAL FLUID DYNAMICS; DYNAMIC PROGRAMMING; FUNCTIONS; MEASUREMENT THEORY; PARTIAL DIFFERENTIAL EQUATIONS; PRESSES (MACHINE TOOLS); SYSTEMS ENGINEERING; VISCOSITY;

STOCHASTIC MODELS;

EID: 69749102885     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spa.2009.05.002     Document Type: Article

References (21)

1. Barles G., Buckdahn R., and Pardoux E. Backward stochastic differential equations and integral-partial differential equations. Stoch. Stoch. Rep. 60 (1997) 57-83
2. Bossy M. Some stochastic particle methods for nonlinear parabolic PDEs. ESAIM Proc. 15 (2005) 18-57
3. Bossy M., and Talay D. A stochastic particle method for the McKean-Vlasov and the Burgers equation. Math. Comput. 217 66 (1997) 157-192
4. Buckdahn R., and Li J. Stochastic differential games and viscosity solutions of Hamilton-Jacobi-Bellman-Isaacs equations. SIAM. J. Control. Optim. 47 1 (2008) 444-475 10.1137/060671954
5. R. Buckdahn, B. Djehiche, J. Li, S. Peng, Mean-field backward stochastic differential equations. A limit approach, Ann. Probab. (2007) (in press). Available online http://www.imstat.org/aop/future_papers.htm
6. Chan T. Dynamics of the McKean-Vlasov equation. Ann. Probab. 22 1 (1994) 431-441
7. Crandall M.G., Ishii H., and Lions P.L. User's guide to viscosity solutions of second order partial differential equations. Bull. Amer. Math. Soc. 27 (1992) 1-67
8. El Karoui N., Peng S., and Quenez M.C. Backward stochastic differential equations in finance. Math. Finance 7 1 (1997) 1-71
9. Ikeda N., and Watanabe S. Stochastic Differential Equations and Diffusion Processes (1989), North Holland-Kodansha, Amsterdam, Tokyo
10. Karatzas I., and Shreve S.E. Brownian Motion and Stochastic Calculus (1987), Springer
11. Kotelenez P. A class of quasilinear stochastic partial differential equations of McKean-Vlasov type with mass conservation. Probab. Theory Related Fields 102 (1995) 159-188
12. Lasry J.M., and Lions P.L. Mean field games. Japan. J. Math. 2 (2007) 229-260 Available online: doi:10.1007/s11537-007-0657-8
13. Méléard S. Asymptotic behaviour of some interacting particle systems; McKean-Vlasov and Boltzmann models. In: Talay D., and Tubaro L. (Eds). Probabilistic Models For Nonlinear PDE's. Lectures Notes in Math. vol. 1627 (1996), Springer-Verlag, Berlin, Heidelberg, New York 42-95
14. Nualart D. The Malliavin Calculus and Related Topics (1995), Springer
15. L. Overbeck, Superprocesses and McKean-Vlasov equations with creation of mass, 1995
16. Pardoux E., and Peng S. Adapted solution of a backward stochastic differential equation. Systems Control Lett. 14 1-2 (1990) 61-74
17. Peng S. In: Yan J., Peng S., Fang S., and Wu L. (Eds). BSDE and Stochastic Optimizations; Topics in Stochastic Analysis (1997), Science Press, Beijing (Chapter 2) (in Chinese)
18. Pra P.D., and Hollander F.D. McKean-Vlasov limit for interacting random processes in random media. J. Statist. Phys. 84 314 (1995) 735-772
19. Sznitman A.S. Nonlinear reflecting diffusion processes, and the propagation of chaos and fluctuations associated. J. Funct. Anal. 56 (1984) 311-336
20. Sznitman A.S. Topics in Propagation of Chaos. Lect. Notes in Math. vol. 1464 (1991), Springer-Verlag, Berlin 165-252
21. Talay D., and Vaillant O. A stochastic particle method with random weights for the computation of statistical solutions of McKean-Vlasov equations. Ann. Appl. Probab. 13 1 (2003) 140-180