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On the optimal filtering of diffusion processes. (English) Zbl 0164.19201

Full Text: DOI
[1] Stratonovich, R. I.: Conditional Markov processes. Theor. Probab. Appl. 5, 156-178 (1960). · Zbl 0106.12401 · doi:10.1137/1105015
[2] Kushner, H. J.: Dynamical equations for optimal nonlinear filtering. J. Differential Equations 2, 179-190 (1967). · Zbl 0158.16801 · doi:10.1016/0022-0396(67)90023-X
[3] Bucy, R. C.: Nonlinear filtering theory. IEEE Trans. Automatic Control 10, 198-199 (1965). · doi:10.1109/TAC.1965.1098109
[4] Shiryaev, A. N.: On stochastic equations in the theory of conditional Markov processes. Theor. Probab. Appl. 11, 179-184 (1966).
[5] Loéve, M.: Probability theory, 3rd edition. Princeton, N. J.: Van Nostrand 1963. · Zbl 0095.12201
[6] Skorohod, A. V.: Studies in the theory of random processes. New York: Addison-Wesley 1965.
[7] Girsanov, I. V.: On transforming a certain class of stochastic processes by absolutely continuous substitutions of measures. Theor. Probab. Appl. 5, 285-301 (1960). · Zbl 0100.34004 · doi:10.1137/1105027
[8] Doob, J. L.: Stochastic processes. New York: Wiley 1953. · Zbl 0053.26802
[9] Blanc-Lapierre, A., and R. Fortet: Théorie des fonctions aléatoires. Paris: Masson et Cie., Ed. 1953; Chapter VII. (Also: D. A. Darling, and A. J. F. Siegert: A systematic approach to a class of problems in the theory of noise and other random phenomena. Part I, IRE Trans. Inform. Theory IT-3, 32-37 (1957)).
[10] Dynkin, E. B.: Markov processes. Berlin-Heidelberg-New York: Springer 1965. · Zbl 0132.37901
[11] ItÔ, K.: On a formula concerning stochastic differentials. Nagoya math. J. 3, 55-65 (1951). · Zbl 0045.07603
[12] - On stochastic differential equations. Mem. Amer. math. Soc. 4 (1951). · Zbl 0054.05803
[13] Wohnham, M.: Some applications of stochastic differential equations to optimal nonlinear filtering. J. Soc. industr. appl. Math. Control 2, 347-369 (1965). · Zbl 0143.19004 · doi:10.1137/0302028
[14] Zakai, M.: The optimal filtering of Markov jump processes in additive white noise. Applied Research Lab, Sylvania Elektronic Systems, Waltham, Mass. R. N. 563, June 1965.