Homogenization of Hamilton-Jacobi-Bellman equations with respect to time-space shifts in a stationary ergodic medium

Communications on Pure and Applied Mathematics

Volumn 61, Issue 6, 2008, Pages 816-847

  Kosygina, Elena ^a   Varadhan, S R S ^b  

^a CITY UNIVERSITY OF NEW YORK   (United States)

^b NEW YORK UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 52349108062     PISSN: 00103640     EISSN: 00103640     Source Type: Journal    
DOI: 10.1002/cpa.20220     Document Type: Article

References (21)

1. Alvarez, O.; Bardi, M. Singular perturbations of nonlinear degenerate parabolic PDEs : a general convergence result. Arch. Ration. Mech. Anal. 170 (2003), no. 1, 17-61.
2. Arisawa, M. Quasi-periodic homogenizations for second-order Hamilton-Jacobi-Bellman equations. Adv. Math. Sci. Appl. 11 (2001), no. 1, 465-480.
3. Bakhvalov, N. S.; Panasenko, G. P. Homogenisation: averaging processes in periodic media. Mathematical problems in the mechanics of composite materials. Mathematics and Its Applications (Soviet Series), 36. Kluwer, Dordrecht, 1989.
4. Bensoussan, A.; Lions, J. L.; Papanicolaou, G. Asymptotic analysis for periodic structures. Studies in Mathematics and Its Applications, 5. North-Holland, Amsterdam, 1978.
5. Braides, A.; Defranceschi, A. Homogenization of multiple integrals. Oxford Lecture Series in Mathematics and Its Applications, 12. Clarendon, Oxford University Press, New York, 1998.
6. Buckdahn, R.; Ichihara, N. Limit theorem for controlled backward SDEs and homogenization of Hamilton-Jacobi-Bellman equations. Appl. Math. Optim. 51 (2005), no. 1, 1-33.
7. Caffarelli, L. A.; Souganidis, P. E.; Wang, L. Homogenization of fully nonlinear, uniformly elliptic and parabolic partial differential equations in stationary ergodic media. Comm. Pure Appl. Math. 58 (2005), no. 3, 319-361.
8. Capuzzo-Dolcetta, I.; Ishii, H. On the rate of convergence in homogenization of Hamilton-Jacobi equations. Indiana Univ. Math. J. 50 (2001), no. 3, 1113-1129.
9. Cioranescu, D.; Donato, P. An introduction to homogenization. Oxford Lecture Series in Mathematics and Its Applications, 17. Clarendon, Oxford University Press, New York, 1999.
10. Evans, L. C. A survey of partial differential equations methods in weak KAM theory. Comm. Pure Appl. Math. 57 (2004), no. 4, 445-480.
11. Fleming, W. H.; Soner, H. M. Controlled Markov processes and viscosity solutions. Applications of Mathematics, 25. Springer, New York, 1993.
12. Ishii, H. Homogenization of the Cauchy problem for Hamilton-Jacobi equations. Stochastic analysis, control, optimization and applications, 305-324. Systems & Control: Foundations & Applications. Birkhäuser, Boston, 1999.
13. Jikov, V. V.; Kozlov, S. M.; Oleǐnik, O. A. Homogenization of differential operators and integral functionals. Springer, Berlin, 1994.
14. Kosygina, E.; Rezakhanlou, F; Varadhan, S. R. S. Stochastic homogenization of Hamilton-Jacobi-Bellman equations. Comm. Pure Appl. Math. 59 (2006), no. 10, 1489-1521.
15. Landim, C.; Olla, S.; Yau, H. T. Convection-diffusion equation with space-time ergodic random flow. Probab. Theory Related Fields 112 (1998), no. 2, 203-220.
16. Lions, P.-L.; Souganidis, P. E. Correctors for the homogenization of Hamilton-Jacobi equations in the stationary ergodic setting. Comm. Pure Appl Math. 56 (2003), no. 10, 1501-1524.
17. Lions, P.-L.; Souganidis, P. E. Homogenization of degenerate second-order PDE in periodic and almost periodic environments and applications. Ann. Inst. H. Poincaré Anal. Non Linéaire 22 (2005), no. 5, 667-677.
18. Lions, P.-L.; Souganidis, P. E. Homogenization of "viscous" Hamilton-Jacobi equations in stationary ergodic media. Comm. Partial Differential Equations 30 (2005), no. 1-3, 335-375.
19. Marchenko, V. A.; Khruslov, E. Ya. Homogenization of partial differential equations. Progress in Mathematical Physics, 46. Birkhäuser, Boston, 2006.
20. Sion, M. On general minimax theorems. Pacific J. Math. 8 (1958), 171-176.
21. Sznitman, A.-S. Brownian motion, obstacles and random media. Springer Monographs in Mathematics. Springer, Berlin, 1998.