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References (31)
-
P. Florchinger, F. Gland (1991)
Time-discretization of the Zakai equation for diffusion processes observed in correlated noiseLecture Notes in Control and Information Sciences, 144
-
P. Kloeden, E. Platen (1977)
The numerical solution of stochastic differential equationsThe Journal of the Australian Mathematical Society. Series B. Applied Mathematics, 20
-
(1990)
Stochastic Evol ution System s.K l uwer A cadem i c Publ i shers -
M. Shubin (1987)
Pseudodifferential Operators and Spectral Theory -
S. Mitter, D. Ocone (1979)
Multiple integral expansions for nonlinear filtering1979 18th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes, 2
-
R. Cameron, W. Martin (1947)
The Orthogonal Development of Non-Linear Functionals in Series of Fourier-Hermite FunctionalsAnnals of Mathematics, 48
-
G. Kallianpur (1979)
Stochastic filtering theoryAdvances in Applied Probability, 11
-
B. Rozovskii (1990)
Stochastic Evolution Systems -
(1979)
Brownian M otion.Spri nger -
S. Lototsky, R. Mikulevičius, B. Rozovskii (1997)
Nonlinear Filtering Revisited: A Spectral ApproachSiam Journal on Control and Optimization, 35
-
R. Lipt︠s︡er, Alʹbert Shiri︠a︡ev (1977)
Statistics of random processes -
A. Budhiraja, G. Kallianpur (1997)
The Feynman-Stratonovich semigroup and stratonovich integral expansions in nonlinear filteringApplied Mathematics and Optimization, 35
-
J. Lo, Ng Sze-Kui (1983)
Optimal Orthogonal Expansion for Estimation I: Signal in White Gaussian Noise -
J. Bennaton (1985)
Discrete time Galerkin approximations to the nonlinear filtering solutionJournal of Mathematical Analysis and Applications, 110
-
R. Mikulevicius, B. Rozovskii (2000)
Fourier--Hermite Expansions for Nonlinear FilteringTheory of Probability and Its Applications, 44
-
P. Moral, J. Jacod, P. Protter (2001)
The Monte-Carlo method for filtering with discrete-time observationsProbability Theory and Related Fields, 120
-
(1995)
Hilbertspacevalued tracesand m ultipleStratonovich integrals with statisticalapplications . ( Dedicated tothem em oryofJerzyNeym an ) -
R. Mikulevicius, B. Rozovskii (2001)
Stochastic Navier-Stokes Equations. Propagation of Chaos and Statistical Moments -
H. Kunita (1981)
Cauchy problem for stochastic partial differential equations arizing in nonlinear filtering theorySystems & Control Letters, 1
-
R. Mikulevicius, B. Rozovskii (1993)
Separation of observations and parameters in nonlinear filteringProceedings of 32nd IEEE Conference on Decision and Control
-
(1991)
Brownian Motion and Stochastic Calculus, Second Ed -
(1998)
Parabolic stochastic PDE's and Wiener chaos -
(1995)
PhD thesi s,U ni versi ty ofSouthern C al i forni a,Los A ngel es -
(2001)
ofm an, and A . Sul em , edi tors, O ptim al C ontrol and PartialD i erentialEquations: In honour ofA l ain Bensoussan,pages258{267 -
(1992)
Liptser and A -
C. Fung, S. Lototsky (1997)
Nonlinear filtering: Separation of parameters and observations using Galerkin approximation and Wiener chaos decomposition -
Kazufumi Ito (1996)
Approximation of the Zakai Equation for Nonlinear FilteringSiam Journal on Control and Optimization, 34
-
and P -
T. Kurtz, P. Protter (1991)
Wong-Zakai Corrections, Random Evolutions, and Simulation Schemes for SDE's -
A. Budhiraja, G. Kallianpur (1996)
Approximations to the solution of the zakai equation using multiple wiener and stratonovich integral expansionsStochastics and Stochastics Reports, 56
-
R. Seydel (2004)
Numerical Integration of Stochastic Differential Equations
- Publisher
- Springer Journals
- Copyright
- Copyright © Inc. by 2003 Springer-Verlag New York
- Subject
- Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
- ISSN
- 0095-4616
- eISSN
- 1432-0606
- DOI
- 10.1007/s00245-002-0760-4
- Publisher site
- See Article on Publisher Site
Abstract
Abstract. An approximation to the solution of a stochastic parabolic equation is constructed using the Galerkin approximation followed by the Wiener chaos decomposition. The result is applied to the nonlinear filtering problem for the time-homogeneous diffusion model with correlated noise. An algorithm is proposed for computing recursive approximations of the unnormalized filtering density and filter, and the errors of the approximations are estimated. Unlike most existing algorithms for nonlinear filtering, the real-time part of the algorithm does not require solving partial differential equations or evaluating integrals. The algorithm can be used for both continuous and discrete time observations. \par
Journal
Applied Mathematics and Optimization – Springer Journals
Published: Mar 12, 2003