Abstract
In this article, we give a brief review of the results of the author and his colleagues working in nonlinear stochastic filtration.
Similar content being viewed by others
REFERENCES
R. S. Liptser and A. N. Shiryaev, Statistics of Random Processes I, General Theory, Springer, New York (1977).
G. Kallianpur, Stochastic Filtering Theory, Applications of Mathematics 13, Springer, New York (1980).
G. Kallianpur and R. L. Karandikar, White Noise Theory of Prediction, Filtering and Smoothing, Stochastic Monographs, 3, Gordon and Breach (1988).
A. Bhatt, G. Kallianpur, and R. L. Karandikar, “Uniqueness and robustness of solutions of measure-valued equations of nonlinear filtering,” Ann. Appl. Probability, 23,No. 4 (1995).
A. Bhatt, G. Kallianpur, and R. L. Karandikar, “Robustness of nonlinear filter,” Stochastic Processes and Applications, 81, 247–254.
H. Kunita, “Stochastic partial differential equations connected with nonlinear filtering,” in: Nonlinear Filtering and Stochastic Control, Eds. S. K. Mitter and A. Moro, Lecture Notes in Mathematics, Springer, New York (1982).
H. Kunita, “The stability and approximation problems in nonlinear filtering theory,” in: Stochastic Analysis, Eds. Eddy Mayer-Wolf, Ely Merzbach, and Adam Schwarz, Academic Press (1991).
H. Kunita, Stochastic Flows and Stochastic Differential Equations, 24, Cambridge Univ. Press, Cambridge (1990).
S. K. Mitter, Lectures on Nonlinear Filtering and Stochastic Control, Lecture Notes in Mathematics, 972, Springer, New York (1982).
E. Pardoux, Equations of Nonlinear Filtering and Applications to Stochastic Control with Partial Observation, Lecture Notes in Mathematics, 972, Springer, New York (1982).
R. Mikulevicius and B. L. Rozovskii, Nonlinear Filtering Revisited: A Spectral Approach, preprint (1993).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kallianpur, G. Nonlinear Stochastic Filtering: A Brief Survey. Journal of Mathematical Sciences 120, 1364–1371 (2004). https://doi.org/10.1023/B:JOTH.0000016054.72184.e4
Issue Date:
DOI: https://doi.org/10.1023/B:JOTH.0000016054.72184.e4