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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:
- [1]
- R. Bellman, Dynamic programming, Princeton Univ. Press, Princeton, NJ, 1957.
- [2]
- M. H. A. Davis, Linear estimation and stochastic control, Chapman \& Hall, London, 1977.
- [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. \textbf{16} (1975), 277--301.
- [5]
- W. H. Fleming and R. W. Rishel, Deterministic and stochastic optimal control, Springer-Verlag, New York, 1975.
- [6]
- F. H. Clarke, Optimization and non-smooth analysis, Wiley-Interscience, New York, 1983.
- [7]
- M. G. Crandall and P. L. Lions, Viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc. \textbf{277} (1984), 1--42.
- [8]
- M. G. Crandall and P. L. Lions, Condition d{\rm '}unicit\'e pour les solutions generalis\'ees des \'equations de Hamilton-Jacobi du premier ordre, C. R. Acad. Sci. Paris S\'er. I. Math. \textbf{292} (1981), 183--186.
- [9]
- M. G. Crandall, H. Ishii, and P. L. Lions, A user{\rm '}s guide to viscosity solutions, Bull. Amer. Math. Soc. (N.S.) \textbf{27} (1992), 1--67.
- [10]
- R. J. Elliott, Viscosity solutions and optimal control, Pitman Res. Notes in Math., vol. 165, Longman, London, 1987.
- [11]
- M. Crandall, Viscosity solutions of partial differential equations, videotape, AMS Progress in Mathematics Series, Amer. Math. Soc., Providence, RI, 1991.
- [12]
- G. Barles and B. Perthame, Exit time problems in optimal control and vanishing viscosity solutions of Hamilton-Jacobi equations, SIAM J. Control Optim. \textbf{26} (1988), 1133--1148.
- [13]
- G. Barles and P. E. Souganidis, Convergence of approximation schemes for fully nonlinear second order equations, J. Asymptotic Anal. \textbf{4} (1991), 271--283.
- [14]
- H. J. Kushner and P. Dupuis, Numerical methods for stochastic control problems in continuous time, Springer-Verlag, New York, 1992.
- [15]
- M. H. A. Davis, V. G. Panas, and T. Zariphopoulou, European option pricing with transaction costs, SIAM J. Control Optim. \textbf{31} (1993), 470--493.
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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