Finite-dimensional filters with nonlinear drift V: Solution to kolmogorov equation arising from linear filtering with non-gaussian initial condition

IEEE Transactions on Aerospace and Electronic Systems

Volumn 33, Issue 4, 1997, Pages 1295-1308

  Liang, Zfflgang ^a,b   Yau, Stephen S T ^a  

^a UNIVERSITY OF ILLINOIS AT CHICAGO   (United States)

^b HARVARD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFERENTIAL EQUATIONS; NUMERICAL ANALYSIS;

KALMAN BUCY FILTERING SYSTEM; KOLMOGOROV EQUATION; NON GAUSSIAN INITIAL CONDITION;

ELECTRIC FILTERS;

EID: 0031259327     PISSN: 00189251     EISSN: None     Source Type: Journal    
DOI: 10.1109/7.625130     Document Type: Article

References (10)

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2. Davis, M. H. A. (1980) On a multiplicative functional transformation arising in nonlinear filtering theory. Z. Wahrsch, Verw. Gebiete, 54 (1980), 125-139.
3. Davis, M. H. A., and Marcus, S. I. (1981) An introduction to nonlinear filtering. In M. Hazewinkel and J. S. Willems (Eds.), The Mathematics of Filtering and Identification and Applications. Dordrecht: Reidel, 1981.
4. Dong, R. T., and Yau, S. S.-T. Existence and uniqueness of Duncan-Mortensen-Zakai equation. In preparation.
5. Folland, G. B. (1976) Mathematical Notes, Introduction to Partial Differential Equations. Cambridge: Princeton University Press, 1976.
6. Hazewinkel, M. (1998) Lectures on linear and nonlinear filtering. In W. Shiehlen and W. Wedig (Eds.), Analysis and Estimation of Stochastic Mechanical Systems (CISM Courses and Lectures 303). New York: Springer, 1998, 103-135.
7. Makowski, A. (1986) Filtering formulae for partially observed linear systems with non-Gaussian initial conditions. Stochastic, 16 (1986), 1-24.
8. Ocone, D. (1980) Topics in nonlinear filtering theory. Ph.D. dissertation, Department of Mathematics, Massachusetts Institute of Technology, Cambridge, 1980.
9. Rozovsky, B. L. (1972) Stochastic partially differential equations arising in nonlinear filtering problems. Uspekhi Math. Nauk, 27 (1972), 213-214 (in Russian).
10. Yau, S. T., and Yau, S. S.-T. (1995) Finite-dimensional filters with nonlinear drift III: Duncan-Mortensen-Zakai equation with arbitrary initial condition for Kalman-Bucy filtering system and Benes filtering system. This issue, p. 1277.