An approximation scheme for the optimal control of diffusion processes
ESAIM: Modélisation mathématique et analyse numérique, Tome 29 (1995) no. 1, pp. 97-122. 
@article{M2AN_1995__29_1_97_0,
     author = {Camilli, Fabio and Falcone, Maurizio},
     title = {An approximation scheme for the optimal control of diffusion processes},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {97--122},
     publisher = {AFCET - Gauthier-Villars},
     address = {Paris},
     volume = {29},
     number = {1},
     year = {1995},
     mrnumber = {1326802},
     zbl = {0822.65044},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1995__29_1_97_0/}
}
TY  - JOUR
AU  - Camilli, Fabio
AU  - Falcone, Maurizio
TI  - An approximation scheme for the optimal control of diffusion processes
JO  - ESAIM: Modélisation mathématique et analyse numérique
PY  - 1995
SP  - 97
EP  - 122
VL  - 29
IS  - 1
PB  - AFCET - Gauthier-Villars
PP  - Paris
UR  - http://www.numdam.org/item/M2AN_1995__29_1_97_0/
LA  - en
ID  - M2AN_1995__29_1_97_0
ER  - 
%0 Journal Article
%A Camilli, Fabio
%A Falcone, Maurizio
%T An approximation scheme for the optimal control of diffusion processes
%J ESAIM: Modélisation mathématique et analyse numérique
%D 1995
%P 97-122
%V 29
%N 1
%I AFCET - Gauthier-Villars
%C Paris
%U http://www.numdam.org/item/M2AN_1995__29_1_97_0/
%G en
%F M2AN_1995__29_1_97_0
Camilli, Fabio; Falcone, Maurizio. An approximation scheme for the optimal control of diffusion processes. ESAIM: Modélisation mathématique et analyse numérique, Tome 29 (1995) no. 1, pp. 97-122. http://www.numdam.org/item/M2AN_1995__29_1_97_0/

[A] M. Akian, 1990, Analyse de l'algorithme multigrille FMGH de résolution d'équations de Hamilton-Jacobi-Bellman, in A. Bensoussan, J.-L Lions (Eds.), Analysis and Optimization of Systems, Lecture Notes in Control and Information Science, n° 144, Springer-Verlag, 113-122. | MR | Zbl

[BS] G. Barles, P. E. Souganidis, 1991, Convergence of approximation schemes for fully non linear second order equations, Asymptotic Analysis, 4, 271-282. | MR | Zbl

[BCM] M.-C. Bancora-Imbert, P.-L. Chow, J.-L. Menaldi, 1989, On the numerical approximation of an optimal correction problem, SIAM J. Sci Statist. Comput., 9, 970-991. | MR | Zbl

[BeS] D. P. Bertsekas, S. Shreve, 1978, Stochastic Optimal Control: the discrete time case, Academic Press, New York. | MR | Zbl

[C] I. Capuzzo-Dolcetta, , 1983, On a discrete approximation of the Hamilton-Jacobi equation of Dynamic Programming, Appl. Math. Optim., 10, 367-377. | MR | Zbl

[CDF] I. Capuzzo-Dolcetta, M. Falcone, 1989, Discrete dynamic programming and viscosity solution of the Bellman equation, Annales de l'Institut H. Poincaré-Analyse non linéaire, 6, 161-184. | Numdam | MR | Zbl

[CF] F. Camilli, M. Falcone, forthcoming.

[CI] I. Capuzzo-Dolcetta, H. Ishii, 1984, Approximate solutions of the Bellman equation of Deterministic Control Theory, Appl. Math. Optim., 11, 161-181. | MR | Zbl

[CIL] M. Crandall, H. Ishii, P.-L. Lions, 1991, A user guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc., 27, 1-67. | MR | Zbl

[FI] M. Falcone, 1987, 1991, A numerical approach to infinite horizon problem,Appl. Math. Optim., 15, 1-13 and 23, 213-214. | MR | Zbl

[F2] M. Falcone, 1985, Numerical solution of optimal control problems, Proceedings of the International Symposium on Numerical Analysis, Madrid.

[FF] M. Falcone, R. Ferretti, 1994, Discrete-time high-order schemes for viscosity solutions of Hamilton-Jacobi-Bellman equations, Numerische Mathematik, 67,315-344. | MR | Zbl

[FIF] B. G. Fitzpatrick, W. H. Fleming, Numerical Methods for an optimal investment/consumption model, to appear on Math. Operation Research. | MR | Zbl

[FS] W. H. Fleming, M. H. Soner, 1993, Controlled Markov processes and viscosity solutions, Springer-Verlag, New York. | MR | Zbl

[GR] R. Gonzales, E. Rofman, 1985, On determmistic control problems : an approximation procedure for the optimal cost(part I and II), SIAM J. Control and Optimization, 23, 242-285. | Zbl

[H] R. Hoppe, 1986, Multi-grid methods for Hamilton-Jacobi-Bellman equations, Numerische Mathematik, 49, 235-254. | MR | Zbl

[IL] H. Ishii, P.-L. Lions, 1990, Viscosity solutions of fully nonlinear second-order elliptic partial differential equations, J. Diff. Eq., 83, 26-78. | MR | Zbl

[K] H. J. Kushner, 1977, Probability methods for approximations in stochastic control and for elliptic equations, Academic Press, New York. | MR | Zbl

[KD] H. J. Kushner, P. Dupuis, 1992, Numerical methods for stochastic control problems in continuous time, Springer Verlag, New York. | MR | Zbl

[Ll] P.-L. Lions, 1983, Optimal control of diffusion processes and Hamilton-Jacobi-Bellman equations part 1 the dynamic programming principle and applications, Comm. Partial Diff. Equations, 8, 1101-1174. | MR | Zbl

[L2] P.-L. Lions, 1983, Optimal control of diffusion processes and Hamilton-Jacobi-Bellman equations part 2 : Viscosity solutions and uniqueness, Comm. Partial Diff. Equations, 8, 1229-1270. | MR | Zbl

[LM] P.-L. Lions, B. Mercier, Approximation numérique des équations de Hamilton-Jacobi-Bellman, RAIRO Anal. Numer., 14, 369-393. | Numdam | MR | Zbl

[M] J.-L. Menaldi, 1989, Some estimates for finite difference approximations, SIAM J. Control Optim., 27, 579-607. | MR | Zbl

[Q] J.-P. Quadrat, 1980, Existence de solution et algorithme de résolutions numériques de problèmes stochastiques dégénérées ou non, SIAM J. Control and Optimization, 18, 199-226. | MR | Zbl

[S] P.-E. Souganidis, 1985, Approximation schemes for viscosity solutions of Hamilton-Jacobi equations, J. Diff. Eq., 57, 1-43. | MR | Zbl

[Su] M. Sun, 1993, Domain decomposition algorithms for solvign Hamilton-Jacobi-Bellman equations, Numerical Func. Anal. and Optim., 14, 145-166. | MR | Zbl