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Computational Nonlinear Stochastic Control based on the FokkerPlanckKolmogorov Equation
, 2008
"... The optimal control of nonlinear stochastic systems is considered in this paper. The central role played by the FokkerPlanckKolmogorov equation in the stochastic control problem is shown under the assumption of asymptotic stability. A computational approach for the problem is devised based on poli ..."
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The optimal control of nonlinear stochastic systems is considered in this paper. The central role played by the FokkerPlanckKolmogorov equation in the stochastic control problem is shown under the assumption of asymptotic stability. A computational approach for the problem is devised based
Sequential data assimilation with a nonlinear quasigeostrophic model using Monte Carlo methods to forecast error statistics
 J. Geophys. Res
, 1994
"... . A new sequential data assimilation method is discussed. It is based on forecasting the error statistics using Monte Carlo methods, a better alternative than solving the traditional and computationally extremely demanding approximate error covariance equation used in the extended Kalman filter. The ..."
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Cited by 782 (22 self)
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. A new sequential data assimilation method is discussed. It is based on forecasting the error statistics using Monte Carlo methods, a better alternative than solving the traditional and computationally extremely demanding approximate error covariance equation used in the extended Kalman filter
A Homotopic Approach to the Solution of the FokkerPlanckKolmogorov Equation
"... A homotopic Galerkin approach to the solution of the FokkerPlanckKolmogorov equation is presented. It is argued that the ideal Hilbert Space to approximate the exact solution, ψ ∗ , is the space L2(dψ ∗ ) where dψ ∗ is the probability measure induced on ℜ n by the solution ψ ∗ itself. Since this s ..."
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A homotopic Galerkin approach to the solution of the FokkerPlanckKolmogorov equation is presented. It is argued that the ideal Hilbert Space to approximate the exact solution, ψ ∗ , is the space L2(dψ ∗ ) where dψ ∗ is the probability measure induced on ℜ n by the solution ψ ∗ itself. Since
Open Access ENG Numeric Solution of the FokkerPlanckKolmogorov Equation
, 2013
"... Copyright © 2013 Claudio Floris et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The solution of an ndimensional stochastic di ..."
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differential equation driven by Gaussian white noises is a Markov vector. In this way, the transition joint probability density function (JPDF) of this vector is given by a deterministic parabolic partial differential equation, the socalled FokkerPlanckKolmogorov (FPK) equation. There exist few exact
CONDENSATION  conditional density propagation for visual tracking
 International Journal of Computer Vision
, 1998
"... The problem of tracking curves in dense visual clutter is challenging. Kalman filtering is inadequate because it is based on Gaussian densities which, being unimodal, cannot represent simultaneous alternative hypotheses. The Condensation algorithm uses "factored sampling", previously appli ..."
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Cited by 1499 (12 self)
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The problem of tracking curves in dense visual clutter is challenging. Kalman filtering is inadequate because it is based on Gaussian densities which, being unimodal, cannot represent simultaneous alternative hypotheses. The Condensation algorithm uses "factored sampling", previously
A Homotopic Galerkin Approach to the Solution of the FokkerPlanckKolmogorov Equation
"... Abstract — In this paper, we present a homotopic Galerkin approach to the solution of the FokkerPlanckKolmogorov equation. We argue that the ideal Hilbert space to approximate the exact solution, ψ ∗ , is the space L2(dΨ ∗ ) where dΨ ∗ is the probability measure induced on ℜ n by the solution ψ ∗ ..."
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Cited by 1 (1 self)
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Abstract — In this paper, we present a homotopic Galerkin approach to the solution of the FokkerPlanckKolmogorov equation. We argue that the ideal Hilbert space to approximate the exact solution, ψ ∗ , is the space L2(dΨ ∗ ) where dΨ ∗ is the probability measure induced on ℜ n by the solution ψ
The Ensemble Kalman Filter: theoretical formulation And Practical Implementation
, 2003
"... The purpose of this paper is to provide a comprehensive presentation and interpretation of the Ensemble Kalman Filter (EnKF) and its numerical implementation. The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it. This paper reviews the ..."
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Cited by 482 (4 self)
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implementation. A program listing is given for some of the key subroutines. The paper also touches upon specific issues such as the use of nonlinear measurements, in situ profiles of temperature and salinity, and data which are available with high frequency in time. An ensemble based optimal interpolation (En
Evaluating collaborative filtering recommender systems
 ACM TRANSACTIONS ON INFORMATION SYSTEMS
, 2004
"... ..."
A unifying formulation of the FokkerPlanckKolmogorov equation for general stochastic hybrid systems
 In Proceedings of the 17th IFAC World Congress
, 2008
"... A general formulation of the FokkerPlanckKolmogorov (FPK) equation for stochastic hybrid systems is presented, within the framework of Generalized Stochastic Hybrid Systems (GSHS). The FPK equation describes the time evolution of the probability law of the hybrid state. Our derivation is based on ..."
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Cited by 6 (0 self)
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A general formulation of the FokkerPlanckKolmogorov (FPK) equation for stochastic hybrid systems is presented, within the framework of Generalized Stochastic Hybrid Systems (GSHS). The FPK equation describes the time evolution of the probability law of the hybrid state. Our derivation is based
The Variational Formulation of the FokkerPlanck Equation
 SIAM J. Math. Anal
, 1999
"... The FokkerPlanck equation, or forward Kolmogorov equation, describes the evolution of the probability density for a stochastic process associated with an Ito stochastic differential equation. It pertains to a wide variety of timedependent systems in which randomness plays a role. In this paper, ..."
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Cited by 285 (22 self)
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The FokkerPlanck equation, or forward Kolmogorov equation, describes the evolution of the probability density for a stochastic process associated with an Ito stochastic differential equation. It pertains to a wide variety of timedependent systems in which randomness plays a role. In this paper
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