Probabilistic approach to singular perturbations of semilinear and quasilinear parabolic PDEs

Nonlinear Analysis, Theory, Methods and Applications

Volumn 35, Issue 7, 1999, Pages 815-831

  Briand, Philippe ^a   Hu, Ying ^a  

^a UNIVERSITÉ BLAISE PASCAL   (France)

Author keywords

BSDEs; FBSDEs; Singular perturbations; Systems of quasilinear PDEs; Systems of semilinear PDEs

Indexed keywords

ASYMPTOTIC STABILITY; CONTROL THEORY; PARTIAL DIFFERENTIAL EQUATIONS; PERTURBATION TECHNIQUES; PROBABILITY; STOCHASTIC CONTROL SYSTEMS; THEOREM PROVING;

BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS (BSDE); ELLIPTIC EQUATIONS; FEYNMAN-KAC FORMULA; FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS (FBSDE); PARABOLIC EQUATIONS; QUASILINEAR EQUATIONS; SEMILINEAR EQUATIONS;

NONLINEAR EQUATIONS;

EID: 0033102271     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(97)00681-0     Document Type: Article

References (13)

1. A. Bensoussan, L. Boccardo, F. Murat, Homogenization of elliptic equations with principal part not in divergence form and hamiltonian with quadratic growth, Commun. Pure Appl. Math. 39 (1986) 769-805.
2. A. Bensoussan, J.L. Lions, G. Papanicolaou, Asymptotic Analysis for Periodic Structures, North-Holland, Amsterdam, 1978.
3. P. Briand, Y. Hu, Stability of BSDEs with random terminal time and homogenization of semilinear elliptic PDEs, J. Funct. Anal. 155 (1998) 455-494.
4. R. Buckdahn, Y. Hu, Probabilistic approach to homogenizations of systems of quasilinear parabolic PDEs with periodic structures, Nonlinear Anal. Theory, Methods, Appl. 32 (1998) 609-619.
5. R. Buckdahn, Y. Hu, S. Peng, Probabilistic approach to homogenizations of systems of semilinear parabolic PDEs, Preprint, 1996.
6. R.W.R. Darling, E. Pardoux, Backwards SDE with random terminal time, and applications to semilinear elliptic PDE, Ann. Proba. 25 (1997) 1135-1159.
7. N. El Karoui, S. Peng, M.C. Quenez, Backward stochastic differential equations in finance, Math. Finance 7 (1997) 1-71.
8. Y. Hu, S. Peng, Solution of forward-backward stochastic differential equations, Probab. Theory Related Fields 103 (1995) 273-283.
9. Y. Hu, S. Peng, A stability theorem of backward stochastic differential equations and its application, C. R. Acad. Sci. Paris, Sér. I Math. 324 (1997) 1059-1064.
10. E. Pardoux, S. Peng, Adapted solution of a backward stochastic differential equation, Systems Control Lett. 14 (1990) 55-61.
11. E. Pardoux, S. Peng, Backward stochastic differential equations and quasilinear parabolic partial differential equations, in: B.L. Rozovskii, R.B. Sowers (Eds.), Stochastic Partial Differential Equations and their Applications, Lecture Notes in Control and Information Sciences 176, Springer, Berlin, 1992.
12. S. Peng, Probabilistic interpretation for systems of quasilinear parabolic partial differential equations, Stochastics Stochastics Rep. 37 (1991) 61-74.
13. J. Ma, P. Protter, J. Yong, Solving forward-backward stochastic differential equations explicitly - a four step scheme, Probab. Theory Related Fields 98 (1994) 339-359.