Probabilistic approach to homogenizations of systems of quasilinear parabolic PDEs with periodic structures

Nonlinear Analysis, Theory, Methods and Applications

Volumn 32, Issue 5, 1998, Pages 609-619

  Buckdahn, Rainer ^a   Hu, Ying ^b  

^a UNIVERSITÉ DE BRETAGNE OCCIDENTALE   (France)

^b UNIVERSITÉ BLAISE PASCAL   (France)

Author keywords

Forward backward SDEs; Homogenizations; Systems of quasilinear parabolic PDEs

Indexed keywords

ASYMPTOTIC STABILITY; FUNCTIONS; MATRIX ALGEBRA; PROBABILITY; PROBLEM SOLVING; RANDOM PROCESSES; THEOREM PROVING;

FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS; GRONWALL'S INEQUALITY; LIPSCHITZ CONSTANTS; QUASILINEAR PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS;

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 0032061556     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(97)00505-1     Document Type: Article

References (7)

1. Ma, J., Protter, P. and Yong, J., Solving forward-backward stochastic differential equations explicitly - a four step scheme. Probab. Theory Relat. Fields, 1994, 98, 339-359.
2. Bensoussan, A., Lions, J. L. and Papanicolaou, G., Asymptotic Analysis for Periodic Structures. North Holland, Amsterdam, 1978.
3. Jikov, V. V., Kozlov, S. M. and Oleinik, O. A., Homogenization of Differential Operators and Integral Functionals. Springer, Berlin, 1991.
4. Buckdahn, R., Hu, Y. and Peng, S., Probabilistic approach to homogenizations of systems of semilinear parabolic PDEs. Preprint.
5. Pardoux, E. and Peng, S., Adapted solution of a backward stochastic differential equation. Syst. Control Lett., 1990, 14, 55-61.
6. Pardoux, E. and Peng, S., Backward stochastic differential equations and quasilinear parabolic partial differential equations, In Stochastic Partial Differential Equations and their Applications, (Lect. Notes Control Inf. Sci.), ed. B. L. Rozovskii and R. B. Sowers, 176. Springer, Berlin, 1992, pp. 200-217.
7. El Karoui, N., Peng, S. and Quenez, M. C., Backward stochastic differential equations in finance. Math. Finance, 1997, 7, 1-71.