BSDE on an infinite horizon and elliptic PDEs in infinite dimension

Nonlinear Differential Equations and Applications

Volumn 14, Issue 5-6, 2007, Pages 825-846

  Hu, Ying ^a   Tessitore, Gianmario ^b  

^a UNIVERSITÉ DE RENNES 1   (France)

^b UNIVERSITY OF MILANO BICOCCA   (Italy)

Author keywords

Backward Stochastic differential equations Elliptic PDEs; Hilbert spaces; Mild solutions

Indexed keywords

EID: 38649101579     PISSN: 10219722     EISSN: 14209004     Source Type: Journal    
DOI: 10.1007/s00030-007-6029-5     Document Type: Article

References (20)

1. J.-P. AUBIN and H. FRANKOWSKA, Set-valued analysis, Birkhäuser, Boston, 1990.
2. P. BRIAND and Y. HU, Stability of BSDEs with random terminal time and homogenization of semilinear elliptic PDEs. J. Funct. Anal. 155 (1998), 455-494.
3. R. BUCKDAHN and S. PENG, Stationary backward stochastic differential equations and associated partial differential equations, Probab. Theory Related Fields 115 (1999), 383-399.
4. S. CERRAI, Second order PDE's in finite and infinite dimensions. A probabilistic approach. Lecture Notes in Mathematics 1762, Springer, Berlin, 2001.
5. G. DA PRATO and J. ZABCZYK, Stochastic Equations in Infinite Dimensions, Cambridge University Press, Cambridge, 1992.
6. G. DA PRATO and J. ZABCZYK, Second Order Partial Differential Equations in Hubert Spaces, Cambridge University Press, Cambridge, 2002.
7. R. W. R. DARLING and E. PARDOUX, Backwards SDE with random terminal time and applications to semilinear elliptic PDE, Ann. Probab. 25 (1997), 1135-1159.
8. M. FUHRMAN and Y. HU, Infinite horizon BSDEs in infinite dimensions with continuous driver and applications. J. Evol. Equ. 6 (2006), 459-484.
9. M. FUHRMAN and G. TESSITORE, Nonlinear Kolmororov equations in infinite dimensional spaces: the backward stochastic differential equations approach and applications to optimal control, Ann. Probab. 30 (2002), 1397-1465.
10. M. FUHRMAN and G. TESSITORE, The Bismut-Elworthy formula for backward SDE's and applications to nonlinear Kolmogorov equations and control, Stochastics Stochastic Rep. 74 (2002), 429-464.
11. M. FUHRMAN and G. TESSITORE, Infinite horizon backward stochastic differential equations and elliptic equations in Hilbert spaces, Ann. Probab. 30 (2004), 607-660.
12. F. GOZZI and E. ROUY, Regular solutions of second-order stationary Hamilton-Jacobi equations, J. Differential Equations 130 (1996), 201-234.
13. F. GOZZI, E. ROUY and A. ŚWIECH, Second order Hamilton-Jacobi equations in Hilbert spaces and stochastic boundary control, SIAM J. Control Optim. 38 (2000), 400-430.
14. F. MASIERO, Infinite horizon stochastic optimal control problems with degenerate noise and elliptic equations in Hilbert spaces. Appl. Meth. Optim, to appear.
15. E. PARDOUX, Backward stochastic differential equations and viscosity solutions of systems of semilinear parabolic and elliptic PDEs of second order, in: Stochastic Analysis and related topics, the Geilo workshop 1996, eds. L. Decreusefond, J. Gjerde, B Øksendal, A. S. Üstünel, 79-127, Progress in Probability 42, Birkhäuser, Boston, 1998.
16. E. PARDOUX and S. PENG, Adapted solution of a backward stochastic differential equation, Systems Control Lett. 14 (1990), 61-74.
17. E. PARDOUX and S. PENG, 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 Inform. Sci. 176, Springer, Berlin, 1992, pp. 200-217.
18. D. REVUZ and M. YOR, Brownian Motion and Continuous Martingales, Springer, Berlin, 1991.
19. M. ROYER, BSDEs with a random terminal time driven by a monotone generator and their links with PDEs, Stochastics Stochastic Rep. 76 (2004) 281-307.
20. A. SWIECH, "Unbounded" second order partial differential equations in infinite-dimensional Hilbert spaces, Comm. Partial Differential Equations 19 (1994) 1999-2036.