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Bulletin of the American Mathematical Society

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

Book Review

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Full text of review: PDF
Book Information:

Author: G. Kallianpur
Title: Stochastic filtering theory
Additional book information: Springer-Verlag, New York, Heidelberg, Berlin, 1980, xvi + 316 pp.,$29.80.

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

  • 1. Deborah F. Allinger and Sanjoy K. Mitter, New results on the innovations problem for nonlinear filtering, Stochastics 4 (1980/81), no. 4, 339–348. MR 609692, 10.1080/17442508108833170
  • 2. V. E. Beneš, Exact finite-dimensional filters for certain diffusions with nonlinear drift, Stochastics 5 (1981), no. 1-2, 65–92. MR 643062, 10.1080/17442508108833174
  • 3. R. W. Brockett, The representation of Lie algebras and estimation theory, Proc. 19th IEEE Conf. on Decision and Control (Dec. 1980).
  • 4. M. H. A. Davis, Pathwise nonlinear filtering, Stochastic Systems: The Mathematics of Filtering and Identification and Applications, (M. Hazewinkel and J. C. Williams, eds. ) NATO Advanced Study Institute Series, Reidel, Dordrecht, 1980.
  • 5. M. H. A. Davis and S. I. Marcus, An introduction to nonlinear filtering, ibid.
  • 6. Masatoshi Fujisaki, G. Kallianpur, and Hiroshi Kunita, Stochastic differential equations for the non linear filtering problem, Osaka J. Math. 9 (1972), 19–40. MR 0336801
  • 7. Arthur Gelb (ed.), Applied optimal estimation, The MIT Press, Cambridge, Mass.-London, 1974. Written by the technical staff of The Analytic Sciences Corporation; Principal authors: Arthur Gelb, Joseph F. Kasper, Jr., Raymond A. Nash, Jr., Charles F. Price and Arthur A. Sutherland, Jr. MR 0345688
  • 8. Kiyosi Itô, Multiple Wiener integral, J. Math. Soc. Japan 3 (1951), 157–169. MR 0044064
  • 9. R. E. Kalman, A new approach to linear filtering and prediction problems, ASME Transactions Part D J. Basic Engrg. 82 (1960), 35-45.
  • 10. R. E. Kalman and R. S. Bucy, New results in linear filtering and prediction theory, Trans. ASME Ser. D. J. Basic Engrg. 83 (1961), 95–108. MR 0234760
  • 11. R. S. Liptser and A. N. Shiryayev, Statistics of random processes. I, Springer-Verlag, New York-Heidelberg, 1977. General theory; Translated by A. B. Aries; Applications of Mathematics, Vol. 5. MR 0474486
  • 12. Paul-A. Meyer, Probability and potentials, Blaisdell Publishing Co. Ginn and Co., Waltham, Mass.-Toronto, Ont.-London, 1966. MR 0205288

Review Information:

Reviewer: Wendell H. Fleming
Journal: Bull. Amer. Math. Soc. 7 (1982), 411-414