Abstract
The present chapter will be concerned with a pair of random processes (θ, ξ) = (θ t , ξ t ), 0 ≤ t ≤ T, where the unobservable component θ is a Markov process with a finite or countable number of states, and the observable process ξ permits the stochastic differential
where W t is a Wiener process.
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Notes and References. 1
Liptser, R.S. and Shiryaev, A.N. (1969): Interpolation and filtering of the jump component of a Markov process. Izv. Akad. Nauk SSSR, Ser. Mat., 33, 4, 901–14
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Shiryaev, A.N. (1966): Stochastic equations of nonlinear filtering of jump Markov processes. Probi. Peredachi Inf., 2, 3, 3–22
Stratonovich, R.L. (1966): Conditional Markov Processes and their Applications to Optimal Control Theory. Izd. MGU, Moscow
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Notes and References. 2
Elliott, R.J., Aggoun, L. and Moore, J.B. (1995): Hidden Markov Models. Springer-Verlag, New York Berl in Heidelberg
Kunita, H. (1971): Ergodic properties of nonlinear filtering processes. In: Spatial Stochastic Processes. K. Alexander and J. Watkins (eds). Birkhäuser, Boston, 233–56
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Liptser, R.S., Shiryaev, A.N. (2001). Optimal Filtering, Interpolation and Extrapolation of Markov Processes with a Countable Number of States. In: Statistics of Random Processes. Applications of Mathematics, vol 5. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-13043-8_10
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DOI: https://doi.org/10.1007/978-3-662-13043-8_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-08366-2
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