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Book Review
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Book Information
Author(s):
W. H. Fleming and \par H. M. Soner
Title:
Controlled Markov processes and viscosity solutions
Additional book information:
Applications of Mathematics, volume 25, Springer-Verlag, New York, 1993, xv+428 pp., US$49.95. ISBN 0-387-97927-1
References:
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- [1]
- R. Bellman, Dynamic programming, Princeton Univ. Press, Princeton, NJ, 1957. MR 0090477 (19:820d)
- [2]
- M. H. A. Davis, Linear estimation and stochastic control, Chapman & Hall, London, 1977. MR 0476099 (57:15678)
- [3]
- L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mischenko, The mathematical theory of optimal processes, Interscience, New York, 1962.
- [4]
- D. Q. Mayne and E. Polak, First order strong variation algorithms for optimal control, J. Optim. Theory Appl. 16 (1975), 277-301. MR 0373284 (51:9484)
- [5]
- W. H. Fleming and R. W. Rishel, Deterministic and stochastic optimal control, Springer-Verlag, New York, 1975. MR 0454768 (56:13016)
- [6]
- F. H. Clarke, Optimization and non-smooth analysis, Wiley-lnterscience, New York, 1983.
- [7]
- M. G. Crandall and P. L. Lions, Viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc. 277 (1984), 1-42. MR 690039 (85g:35029)
- [8]
- -, Condition d'unicité pour les solutions généralisées des équations de Hamilton-Jacobi du premier ordre, C. R. Acad. Sci. Paris Sér. I. Math. 292 (1981), 183-186. MR 610314 (82c:49020)
- [9]
- M. G. Crandall, H. Ishii, and P. L. Lions, A user's guide to viscosity solutions, Bull. Amer. Math. Soc. (N.S.) 27 (1992), 1-67. MR 1118699 (92j:35050)
- [10]
- R. J. Elliott, Viscosity solutions and optimal control, Pitman Res. Notes in Math., vol. 165, Longman, London, 1987. MR 913938 (89a:49028)
- [11]
- M. Crandall, Viscosity solutions of partial differential equations, videotape, AMS Progress in Mathematics Series, Amer. Math. Soc., Providence, RI, 1991. MR 1146680 (92k:35001)
- [12]
- G. Barles and B. Perthame, Exit time problems in optimal control and vanishing viscosity solutions of Hamilton-Jacobi equations, SIAM J. Control Optim. 26 (1988), 1133-1148. MR 957658 (89i:49021)
- [13]
- G. Barles and P. E. Souganidis, Convergence of approximation schemes for fully nonlinear second order equations, J. Asymptotic Anal. 4 (1991), 271-283. MR 1115933 (92d:35137)
- [14]
- H. J. Kushner and P. Dupuis, Numerical methods for stochastic control problems in continuous time, Springer-Verlag, New York, 1992. MR 1217486 (94e:93005)
- [15]
- M. H. A. Davis, V. G. Panas, and T. Zariphopoulou, European option pricing with transaction costs, SIAM J. Control Optim. 31 (1993), 470-493. MR 1205985 (94d:90012)
Additional Information:
Reviewer(s):
M. H. A.
Davis
Review Information:
Journal:
Bull. Amer. Math. Soc.
31
(1994),
75-85.
DOI:
10.1090/S0273-0979-1994-00480-X
PII:
S 0273-0979(1994)00480-X
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