Differentiability of backward stochastic differential equations in Hilbert spaces with monotone generators

Applied Mathematics and Optimization

Volumn 57, Issue 2, 2008, Pages 149-176

  Briand, Philippe ^a   Confortola, Fulvia ^b  

^a UNIVERSITÉ DE RENNES 1   (France)

^b POLITECNICO DI MILANO   (Italy)

Author keywords

Backward stochastic differential equations; Kolmogorov equations; Monotone operators

Indexed keywords

KOLMOGOROV EQUATIONS; MONOTONE OPERATORS;

HILBERT SPACES; MATHEMATICAL OPERATORS; STOCHASTIC CONTROL SYSTEMS;

DIFFERENTIAL EQUATIONS;

EID: 40949165056     PISSN: 00954616     EISSN: 14320606     Source Type: Journal    
DOI: 10.1007/s00245-007-9014-9     Document Type: Article

References (21)

1. Bensoussan, A.: Stochastic control by functional analysis methods. In: Studies in Mathematics and its Applications, vol. 11. North-Holl, Amsterdam (1982)
2. Bensoussan, A., Lions, J.L.: Application of variational inequalities in stochastic control. In: Studies in Mathematics and its Applications, vol. 12. North-Holland, Amsterdam (1982)
3. p solutions of backward stochastic differential equations. Stoch. Process. Appl. 108(1), 109-129 (2003)
4. Cerrai, S.: Second order PDE's in finite and infinite dimensions. A probabilistic approach. Probab. Theory Relat. Fields 115, 383-399 (1999)
5. Da Prato, G., Zabczyk, J.: Stochastic Equations in Infinite Dimensions Encyclopedia of Mathematics and its Applications, vol. 44. Cambridge University Press, Cambridge (1992)
6. El Karoui, N.: Backward stochastic differential equations a general introduction. In: El Karoui, N., Mazliak, L. (eds.) Backward Stochastic Differential Equations. Pitman Research Notes in Mathematics Series, vol. 364, pp. 7-26. Longman, Harlow (1997)
7. El Karoui, N., Peng, S., Quenez, M.C.: Backward stochastic differential equations in finance. Math. Finance 7(1), 1-71 (1997)
8. Fleming, W.H., Soner, H.M.: Controlled Markov Processes and Viscosity Solutions. Springer, Berlin (1993)
9. Fuhrman, M., Tessitore, G.: Nonlinear Kolmogorov equations in infinite dimensional spaces: the backward stochastic differential equations approach and applications to optimal control. Ann. Probab. 30(3), 1397-1465 (2002)
10. Fuhrman, M., Tessitore, G.: Infinite horizon backward stochastic differential equations and elliptic equations in Hilbert spaces. Ann. Probab. 32(1B), 607-660 (2004)
11. Gozzi, F., Rouy, E.: Regular solutions of second-order stationary Hamilton-Jacobi equations. J. Differ. Equ. 130(1), 201-234 (1996)
12. Ma, J., Yong, J.: Forward-Backward Stochastic Differential Equations and their Applications. Lecture Notes in Mathematics, vol. 1702. Springer, Berlin (1999)
13. Pardoux, E.: Backward stochastic differential equations and viscosity solutions of systems of semilinear parabolic and elliptic PDEs of second order. In: Stochastic Analysis and Related Topics, VI, Geilo, 1996. Progr. Probab., vol. 42, pp. 79-127. Birkhser Boston, Boston (1998)
14. Pardoux, E.: BSDEs, weak convergence and homogenization of semilinear PDEs. In: Nonlinear Analysis, Differential Equations and Control, Montreal, QC, 1998. NATO Sci. Ser. C Math. Phys. Sci., vol. 528, pp. 503-549. Kluwer Acad. Publ., Dordrecht (1999)
15. Pardoux, E., Peng, S.: Adapted solution of a backward stochastic differential equation. Syst. Control Lett. 14, 55-61 (1990)
16. Pardoux, E., Peng, S.: Backward stochastic differential equations and quasilinear parabolic partial differential equations. In: Rozowskii, B.L., Sowers, R.B. (eds.) Stochastic Partial Differential Equations and their Applications. Lecture Notes in Control Inf. Sci., vol. 176, pp. 200-217. Springer, Berlin (1992)
17. Peng, S.: Probabilistic interpretation for systems of quasilinear parabolic partial differential equations. Stochastics 37, 61-74 (1991)
18. Peng, S.: A nonlinear Feynman-Kac formula and applications. In: Control Theory, Stochastic Analysis and Applications, pp. 173-184. World Sci. Publishing, River Edge (1991)
19. Peng, S.: Stochastic Hamilton-Jacobi-Bellman equations. SIAM J. Control Optim. 30, 284-304 (1992)
20. Peng, S.: A generalized dynamic programming principle and Hamilton-Jacobi-Bellman equation. Stochastics 38, 119-134 (1992)
21. Zabczyk, J.: Parabolic equations on Hilbert spaces. In: Da Prato, G. (ed.) Stochastic PDE's and Kolmogorov Equations in Infinite Dimensions. Lecture Notes in Mathematics, vol. 1715, pp. 117-213. Springer, Berlin (1999)