×

zbMATH — the first resource for mathematics

Optimal control of diffusion processes and Hamilton-Jacobi-Bellman equations. II: Viscosity solutions and uniqueness. (English) Zbl 0716.49023
This second part of the paper is also covered by the review of the first part, ibid. 8, No.10, 1101-1174 (1983; Zbl 0716.49022). For part III see “Nonlinear partial differential equations and their applications”, Res. Notes Math. 93, 95-205 (1983; Zbl 0716.49024).

MSC:
49K45 Optimality conditions for problems involving randomness
93E20 Optimal stochastic control
49L20 Dynamic programming in optimal control and differential games
49L25 Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games
35R60 PDEs with randomness, stochastic partial differential equations
60J60 Diffusion processes
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Alexandrov A. D., Ucen. Zap. Leningrad Gos. Univ., 37 pp 3– (1939)
[2] Bellman R., Dynamic programming (1957)
[3] Bensoussan A., Applcations des inéquations variaationnelles en contröle stochastique. (1978)
[4] Busemann H., Convex surfaces (1958) · Zbl 0196.55101
[5] Crandall M. G., To appear in Trans. Amer. Math. Soc.. (1958)
[6] Crandall M. G., Cr. Acad. Sc. Paris 252 pp 183– (1981)
[7] Crandall M. G., To appear in Trans. Amer. Math. Sco.. 252 (1981)
[8] Evens L. C., Ind. Univ. Math. J. 27 pp 875– (1978) · Zbl 0408.35037 · doi:10.1512/iumj.1978.27.27059
[9] Evens L. C., Israel. J. Math. 36 pp 225– (1981) · Zbl 0454.35038 · doi:10.1007/BF02762047
[10] Evens L. C., Comm. Pure. Appl. Math. 36 (1982)
[11] Evens L. C., Preprint 36 (1982)
[12] Evens L. C., Cr. Acad. Sc. Paris 290 pp 1049– (1980)
[13] Fleming W. H., Deterministic and stochastic optimal control (1975) · Zbl 0323.49001 · doi:10.1007/978-1-4612-6380-7
[14] K. Ito : To appear
[15] Krylov N. V., Control of diffusion processes (1980) · Zbl 0432.60049 · doi:10.1007/978-1-4612-6051-6
[16] Krylov N. V., I. Math. Ussr Sbornik 34 pp 765– (1978) · Zbl 0445.35067 · doi:10.1070/SM1978v034n06ABEH001356
[17] Krylov N. V., II. Math. USSR Sbornik 35 pp 351– (1979) · Zbl 0439.60079 · doi:10.1070/SM1979v035n03ABEH001487
[18] Krylov N. V., Sib. Mat. J. 1976 pp 226– (1979)
[19] Optimal control of diffusion processes and Hamilton-Jacobi-Bellman equations. Part 1 : The Dynamic Programming Principle and applications.Preprint.
[20] Lions P. L., Generalized solutions of Hamiton–Jacobi equations (1980)
[21] Lions P. L., Optimal stochastic control of diffusion type processes and Hamilton–Jacobi–Bellman equations, In Proceedings IFIP Conf. on Optimal Stochastic Control and Filtering in Cocoyoc (1982) · Zbl 0509.93068
[22] Lions P. L., Fully nonlinear elliptic equations and applications. In Proceedings of the Function Spaces and Applications Conference in Pisek (1982) · Zbl 0501.35031
[23] Lions P. L., Preprint (1982)
[24] Lions P. L., Acta. Math. 146 pp 151– (1981) · Zbl 0467.49016 · doi:10.1007/BF02392461
[25] Lions P. L., Ann. de Toulose III 146 pp 59– (1981)
[26] Lions P. L., Comm. Pure. Appl. Math. 34 pp 121– (1981) · doi:10.1002/cpa.3160340106
[27] Lions P. L., To appear in Proc. Japan Acad.. 34 (1981)
[28] P. L. Lions, G. Papanicolaou and S. R. S. Varadhan: To appear
[29] Mignot F., J. Funct. Anal. 22 pp 130– (1976) · Zbl 0364.49003 · doi:10.1016/0022-1236(76)90017-3
[30] Nisio M., Proc. Third USSR–Japan Symp. Proba. Theory. Lecture Notes in Math.
[31] Nisio M., Jap. J. Math. 1 pp 159– (1975)
[32] Nisio M., ISI Lecture Notes 9 (1981)
[33] Nisio M., Publ, R.I.M.S. Kyoto Univ. 12 pp 513– (1976) · Zbl 0364.93039 · doi:10.2977/prims/1195190727
[34] Nisio M., Proc. Int. Symp. SDE. Kyoto (1976)
[35] Stein E., Singular integrals and differentiability properties of functions (1970) · Zbl 0207.13501
[36] Stein E., Comm. Pure. Appl. Math. 25 pp 651– (1972) · Zbl 0344.35041 · doi:10.1002/cpa.3160250603
[37] Stroock D. W., Multidimensional diffusion processes · Zbl 0426.60069 · doi:10.1007/3-540-28999-2
[38] N. S. Trudinger: Elliptic equations in non–divergence form. Preprint · Zbl 0555.35040
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.