Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.


Full text of review: PDF   This review is available free of charge.
Book Information:

Author: 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 [Enhancements On Off] (What's this?)

  • [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)

Review Information:

Reviewer: M. H. A. Davis
Journal: Bull. Amer. Math. Soc. 31 (1994), 75-85
DOI: https://doi.org/10.1090/S0273-0979-1994-00480-X
American Mathematical Society