Abstract
The second part was devoted to the rms-optimal filtration of the states of the Markov jump processes in continuous time which generalize the finite-state Markov processes. Equations for the conditional expectations and the probability density function were obtained. The Zakai equations for the corresponding unnormalized characteristics also were obtained. The proposed best nonlinear estimates were compared by way of a numerical example with the best linear estimates of the Kalman–Bucy filtration.
Similar content being viewed by others
REFERENCES
Borisov, A.V., Analysis and Estimation of the States of Special Jump Markov Processes. I. Martingale Representation, Avtom. Telemekh., 2004, no. 1, pp. 50–65.
Elliott, R.J., Aggoun, L., and Moore, J.B., Hidden Markov Models: Estimation and Control, Berlin: Springer-Verlag, 1995.
Loëve, M., Probability Theory, Princeton: Van Nostrand, 1963. Translated under the title Teoriya veroyatnostei, Moscow: Inostrannaya Literatura, 1962.
Elliott, R.J., Stochastic Calculus and Applications, New York: Springer, 1982. Translated under the title Stokhasticheskii analiz and ego prilozheniya, Moscow: Mir, 1986.
Liptser, R.Sh. and Shiryaev, A.N., Statistika sluchainykh protsessov (nelineinaya fil'tratsiya i smezhnye voprosy), Moscow: Nauka, 1974. Translated under the title Statistics of Random Processes, Berlin: Springer-Verlag, 1978.
Kloeden, P. and Platen, E., The Numerical Solution of Stochastic Differential Equations, Berlin: Springer-Verlag, 1992.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Borisov, A.V. Analysis and Estimation of the States of Special Jump Markov Processes. II. Optimal Filtration in Wiener Noise. Automation and Remote Control 65, 741–754 (2004). https://doi.org/10.1023/B:AURC.0000028322.97957.ca
Issue Date:
DOI: https://doi.org/10.1023/B:AURC.0000028322.97957.ca