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Problemy Peredachi Informatsii, 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.
Received: 20.01.1966
Bibliographic databases:
UDC: 519.27
Language: Russian
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://mathscinet.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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  • https://www.mathnet.ru/eng/ppi/v2/i3/p3
    Erratum
    This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Проблемы передачи информации Problems of Information Transmission
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