Book Review
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MathSciNet review:
1567375
Full text of review:
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Book Information:
Author:
G. Kallianpur
Title:
Stochastic filtering theory
Additional book information:
Springer-Verlag, New York, Heidelberg, Berlin, 1980, xvi + 316 pp.,$29.80.
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, DOI 10.1080/17442508108833170
V. E. Beneš, Exact finite-dimensional filters for certain diffusions with nonlinear drift, Stochastics 5 (1981), no. 1-2, 65–92. MR 643062, DOI 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.
Masatoshi Fujisaki, G. Kallianpur, and Hiroshi Kunita, Stochastic differential equations for the non linear filtering problem, Osaka Math. J. 9 (1972), 19–40. MR 336801
Arthur Gelb (ed.), Applied optimal estimation, 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
Kiyosi Itô, Multiple Wiener integral, J. Math. Soc. Japan 3 (1951), 157–169. MR 44064, DOI 10.2969/jmsj/00310157
9. R. E. Kalman, A new approach to linear filtering and prediction problems, ASME Transactions Part D J. Basic Engrg. 82 (1960), 35-45.
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 234760
R. S. Liptser and A. N. Shiryayev, Statistics of random processes. I, Applications of Mathematics, Vol. 5, Springer-Verlag, New York-Heidelberg, 1977. General theory; Translated by A. B. Aries. MR 0474486
Paul-A. Meyer, Probability and potentials, Blaisdell Publishing Co. [Ginn and Co.], Waltham, Mass.-Toronto, Ont.-London, 1966. MR 0205288
- 1.
- D. F. Allinger and S. K. Mitter, New results on the innovations problem for non-linear filtering, Stochastics 4 (1981), 339-348. MR 0609692
- 2.
- V. E. Benes, Exact finite dimensional filters for certain diffusions with nonlinear drift, Stochastics 4 (1981). MR 643062
- 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.
- M. Fujisaki, G. Kallianpur, and H. Kunita, Stochastic differential equations for the nonlinear filtering problem, Osaka J. Math. 9 (1972), 19-40. MR 336801
- 7.
- A. Gelb (ed.), Applied optimal estimation, MIT Press, Cambridge, Mass., 1974. MR 345688
- 8.
- K. Itô, Multiple Wiener integrals, J. Math. Soc. Japan 3 (1951), 157-169. MR 44064
- 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, ASME Transactions Part D J. Basic Engrg. (1961), 95-108. MR 234760
- 11.
- R. Sh. Liptser and A. N. Shiryayev, Statistics of random processes (2 vols. ), Springer-Verlag, New York, 1977. MR 474486
- 12.
- P. A. Meyer, Probability and potentials, Blaisdell, Waltham, Mass., 1966. MR 205288
Review Information:
Reviewer:
Wendell H. Fleming
Journal:
Bull. Amer. Math. Soc.
7 (1982), 411-414
DOI:
https://doi.org/10.1090/S0273-0979-1982-15051-0
