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Despite being a foundational concept of modern systems theory, there have been few studies on observability of non-linear stochastic systems under partial observations.
An extension of tietze’s theorem
J. Dugundji · 1951
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A new approach to linear filtering and prediction problems
R. E. Kalman · 1960
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Merging of opinions with increasing information
D. Blackwell and L. Dubins · 1962
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Information-type measures of difference of probability distributions and indirect observation
I. Csiszár · 1967
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Asymptotic behavior of the nonlinear filtering errors of markov processes
H. Kunita · 1971
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Introduction to Stochastic Control Theory
H.J. Kushner · 1972
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An information-theoretical proof of limit theorems for reversible Markov processes
J. Fritz · 1973
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Dual effect, certainty equivalence, and separation in stochastic control
Y. Bar-Shalom and E. Tse · 1974
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Nonlinear controllability and observability
R. Hermann and A. Krener · 1977
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Detectability and stabilizability of time-varying discrete-time linear systems
B. D. O. Anderson and J. B. Moore · 1981
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Observability of autonomous discrete time non-linear systems: a geometric approach
H. Nijmeijer · 1982
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A concept of local observability
E. D. Sontag · 1984
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Probability and Measure
P. Billingsley · 1986
Earlier work this paper cites.
Linear Stochastic Systems
P. E. Caines · 1988
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On merging of probabilities
A. D’Aristotile, P. Diaconis, and D. Freedman · 1988
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Information theory and martingales
A. R. Barron · 1991
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Discrete-time filtering for linear systems with non-Gaussian initial conditions: asymptotic behavior of the difference between the MMSE and LMSE estimates
R.B Sowers and A.M. Makowski · 1992
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White-noise representations in stochastic realization theory
V. S. Borkar · 1993
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Markov Chains and Stochastic Stability
S. P. Meyn and R. Tweedie · 1993
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Finite-memory suboptimal design for partially observed markov decision processes
C. C. White III and W. T. Scherer · 1994
Cited alongside, same era.
Convergence of probability measures
P. Billingsley · 1999
Cited alongside, same era.
Linear Systems Theory and Design
C. T. Chen · 1999
Cited alongside, same era.
Relative entropy and error bounds for filtering of markov processes
J.M.C. Clark, D. L. Ocone, and C. Coumarbatch · 1999
Cited alongside, same era.
Asymptotic stability of beneš filters
D. L. Ocone · 1999
Cited alongside, same era.
Limits of information, Markov chains, and projections
A. R. Barron · 2000
Cited alongside, same era.
Real Analysis and Probability
Thinning, entropy, and the law of thin numbers
P. Harremoës, O. Johnson, and I. Kontoyiannis · 2010
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Observability and reconstructibility of hidden markov models: Implications for control and network congestion control
A.R. Liu and R.R. Bitmead · 2010
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Nonlinear filtering and systems theory
R. van Handel · 2010
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Entropy and information theory
R .M. Gray · 2011
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Stochastic observability, reconstructibility, controllability, and reachability
A. R. Liu · 2011
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Controlled stochastic processes
I. I. Gihman and A. V. Skorohod · 2012
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R. M. Dudley · 2002
Cited alongside, same era.
Observability of linear stochastic uncertain systems
V.A. Ugrinovskii · 2003
Cited alongside, same era.
On a role of predictor in the filtering stability
P. Chigansky and R. Liptser · 2006
Cited alongside, same era.
Real and Complex Analysis
W. Rudin · 2006
Cited alongside, same era.
Measure Theory
V. I. Bogachev · 2007
Cited alongside, same era.
Discrete time nonlinear filters with informative observations are stable
R. van Handel · 2008
Cited alongside, same era.
A partial history of the early development of continuous-time nonlinear stochastic systems theory
H. J. Kushner · 2014
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On optimal zero-delay coding of vector markov sources
T. Linder and S. Yüksel · 2014
Later among the works it cites.
Partially observable total-cost Markov decision process with weakly continuous transition probabilities
E.A. Feinberg, P.O. Kasyanov, and M.Z. Zgurovsky · 2016
Later among the works it cites.
Weak Feller property of non-linear filters
A.D Kara, N. Saldi, and S. Yüksel · 2019
Closest in time.
Robustness to incorrect priors in partially observed stochastic control
A.D Kara and S. Yüksel · 2019
Closest in time.
What is the Lagrangian for nonlinear filtering?
J.-W. Kim, P. G. Mehta, and S. P. Meyn · 2019
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Stability of non-linear filter for deterministic dynamics
A.S. Reddy and A. Apte · 2019
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Planning in observable pomdps in quasipolynomial time
N. Golowich, A. Moitra, and D. Rohatgi · 2022
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A.D Kara and S. Yüksel · 2022
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Near optimality of finite memory feedback policies in partially observed markov decision processes
A.D Kara and S. Yüksel · 2022
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Duality for nonlinear filtering i: Observability
J.-W. Kim and P. G. Mehta · 2022
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Robustness to incorrect priors and controlled filter stability in partially observed stochastic control
C. McDonald and S. Yüksel · 2022
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