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Probl. Peredachi Inf., 1966, Volume 2, Issue 3, Pages 3–22 (Mi ppi1954)  

This article is cited in 4 scientific papers (total in 4 papers)

Stochastic Equations of Nonlinear Filtering of Markovian Jump Processes

A. N. Shiryaev


Abstract: Let $(\theta_t,\eta_t)$ be a Markov process where $\theta_t$ is a non-observable component which is a Markovian jump process, and $\eta_t$ is the observable component satisfying the equation
$$ d\eta_t=A(\theta_t,\eta_t,t)dt+B(\eta_t,t)dW_t, \eta_0=0 $$
. This paper derives stochastic equations which the a posteriori probabilities $\pi_t(\mathfrak A)=\mathbf P\{\theta_t\in\mathfrak A/\eta(\tau), \tau\leq t\}$ satisfy [see Eq. (4)] and which are sufficient statistics in various problems in nonlinear filtering, extrapolation, in optimal control problems, pattern recognition, etc.

Full text: PDF file (2836 kB)

English version:
Problems of Information Transmission, 1966, 2:3, 1–18

Bibliographic databases:

UDC: 519.27
Received: 20.01.1966

Citation: A. N. Shiryaev, “Stochastic Equations of Nonlinear Filtering of Markovian Jump Processes”, Probl. Peredachi Inf., 2:3 (1966), 3–22; Problems Inform. Transmission, 2:3 (1966), 1–18

Citation in format AMSBIB
\Bibitem{Shi66}
\by A.~N.~Shiryaev
\paper Stochastic Equations of Nonlinear Filtering of Markovian Jump Processes
\jour Probl. Peredachi Inf.
\yr 1966
\vol 2
\issue 3
\pages 3--22
\mathnet{http://mi.mathnet.ru/ppi1954}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=204199}
\zmath{https://zbmath.org/?q=an:0271.60082}
\transl
\jour Problems Inform. Transmission
\yr 1966
\vol 2
\issue 3
\pages 1--18


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    Citing articles on Google Scholar: Russian citations, English citations
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    Erratum

    This publication is cited in the following articles:
    1. R. Sh. Liptser, A. N. Shiryaev, “Interpolation and filtering of a jump-like component of a Markov process”, Math. USSR-Izv., 3:4 (1969), 853–865  mathnet  crossref  mathscinet  zmath
    2. R. Sh. Liptser, A. N. Shiryaev, “On the density of probability measures of diffusion-type processes”, Math. USSR-Izv., 3:5 (1969), 1055–1066  mathnet  crossref  mathscinet  zmath
    3. R. Sh. Liptser, A. N. Shiryaev, “On the absolute continuity of measures corresponding to processes of diffusion type relative to a Wiener measure”, Math. USSR-Izv., 6:4 (1972), 839–882  mathnet  crossref  mathscinet  zmath
    4. V. V. Khutortsev, “On asymptotic description of a probabilistic change-point model for a two-state discrete Markov process”, Problems Inform. Transmission, 45:3 (2009), 232–241  mathnet  crossref  mathscinet  zmath  isi
  • Проблемы передачи информации Problems of Information Transmission
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