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Problemy Peredachi Informatsii, 1966, Volume 2, Issue 3, Pages 3–22
(Mi ppi1954)
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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
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
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