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Volumn 43, Issue 2, 2005, Pages 643-669

Asymptotic stability of the Wonham filter: Ergodic and nonergodic signals

Author keywords

Nonlinear filtering; Stability; Wonham filter

Indexed keywords

COMPUTATION THEORY; FUNCTIONS; MARKOV PROCESSES; MATHEMATICAL MODELS; MATHEMATICAL TRANSFORMATIONS; MATRIX ALGEBRA; PROBABILITY; PROBLEM SOLVING; RANDOM PROCESSES; SIGNAL PROCESSING; SYSTEM STABILITY; VECTORS;

EID: 16244416202     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012902416924     Document Type: Article
Times cited : (51)

References (45)
  • 1
    • 0032236910 scopus 로고    scopus 로고
    • Exponential stability for nonlinear filtering of diffusion processes in a noncompact domain
    • R. ATAR, Exponential stability for nonlinear filtering of diffusion processes in a noncompact domain, Ann. Probab., 26 (1998), pp. 1552-1574.
    • (1998) Ann. Probab. , vol.26 , pp. 1552-1574
    • Atar, R.1
  • 3
    • 0030833508 scopus 로고    scopus 로고
    • Lyapunov exponents for finite state nonlinear filtering
    • R. ATAR AND O. ZEITOUNI, Lyapunov exponents for finite state nonlinear filtering, SIAM J. Control Optim., 35 (1997), pp. 36-55.
    • (1997) SIAM J. Control Optim. , vol.35 , pp. 36-55
    • Atar, R.1    Zeitouni, O.2
  • 4
    • 0242446246 scopus 로고    scopus 로고
    • Robustness of Zakai's equation via Feynman-Kac representations
    • W. M. McE-neaney, G. Yin, and Q. Zhang, eds., Birkhäuser Boston, Boston
    • R. ATAR, F. VIENS, AND O. ZEITOUNI, Robustness of Zakai's equation via Feynman-Kac representations, in Stochastic Analysis, Control, Optimization, and Applications, W. M. McE-neaney, G. Yin, and Q. Zhang, eds., Birkhäuser Boston, Boston, 1998, pp. 339-352.
    • (1998) Stochastic Analysis, Control, Optimization, and Applications , pp. 339-352
    • Atar, R.1    Viens, F.2    Zeitouni, O.3
  • 5
    • 0004800539 scopus 로고
    • Estimation and control for linear, partially observable systems with non-Gaussian initial distribution
    • V. E. BENEŠ AND I. KARATZAS, Estimation and control for linear, partially observable systems with non-Gaussian initial distribution, Stochastic Process Appl., 14 (1983), pp. 233-248.
    • (1983) Stochastic Process Appl. , vol.14 , pp. 233-248
    • Beneš, V.E.1    Karatzas, I.2
  • 6
    • 0034437888 scopus 로고    scopus 로고
    • Markov property and ergodicity of the nonlinear filter
    • A. G. BHATT, A. BUDHIRAJA, AND R. L. KARANDIKAR, Markov property and ergodicity of the nonlinear filter, SIAM J. Control Optim., 39 (2000), pp. 928-949.
    • (2000) SIAM J. Control Optim. , vol.39 , pp. 928-949
    • Bhatt, A.G.1    Budhiraja, A.2    Karandikar, R.L.3
  • 7
    • 0041406094 scopus 로고    scopus 로고
    • Ergodic properties of the nonlinear filter
    • A. BUDHIRAJA, Ergodic properties of the nonlinear filter, Stochastic Process Appl., 95 (2001), pp. 1-24.
    • (2001) Stochastic Process Appl. , vol.95 , pp. 1-24
    • Budhiraja, A.1
  • 8
    • 0036387411 scopus 로고    scopus 로고
    • On invariant measures of discrete time filters in the correlated signal-noise case
    • A. BUDHIRAJA, On invariant measures of discrete time filters in the correlated signal-noise case, Ann. Appl. Probab., 12 (2002), pp. 1096-1113.
    • (2002) Ann. Appl. Probab. , vol.12 , pp. 1096-1113
    • Budhiraja, A.1
  • 9
    • 0031139499 scopus 로고    scopus 로고
    • Exponential stability of discrete-time filters for bounded observation noise
    • A. BUDHIRAJA AND D. OCONE, Exponential stability of discrete-time filters for bounded observation noise, Systems Control Lett., 30 (1997), pp. 185-193.
    • (1997) Systems Control Lett. , vol.30 , pp. 185-193
    • Budhiraja, A.1    Ocone, D.2
  • 10
    • 0005648615 scopus 로고    scopus 로고
    • Exponential stability in discrete-time filtering for nonergodic signals
    • A. BUDHIRAJA AND D. OCONE, Exponential stability in discrete-time filtering for nonergodic signals, Stochastic Process. Appl., 82 (1999), pp. 245-257.
    • (1999) Stochastic Process. Appl. , vol.82 , pp. 245-257
    • Budhiraja, A.1    Ocone, D.2
  • 11
    • 0032166438 scopus 로고    scopus 로고
    • Robustness of nonlinear filters over the infinite time interval
    • A. BUDHIRAJA AND H. J. KUSHNER, Robustness of nonlinear filters over the infinite time interval, SIAM J. Control Optim., 36 (1998), pp. 1618-1637.
    • (1998) SIAM J. Control Optim. , vol.36 , pp. 1618-1637
    • Budhiraja, A.1    Kushner, H.J.2
  • 12
    • 0033184461 scopus 로고    scopus 로고
    • Approximation and limit results for nonlinear filters over an infinite time interval
    • A. BUDHIRAJA AND H. J. KUSHNER, Approximation and limit results for nonlinear filters over an infinite time interval, SIAM J. Control Optim., 37 (1999), pp. 1946-1979.
    • (1999) SIAM J. Control Optim. , vol.37 , pp. 1946-1979
    • Budhiraja, A.1    Kushner, H.J.2
  • 13
    • 0034542098 scopus 로고    scopus 로고
    • Approximation and limit results for nonlinear filters over an infinite time interval. II. Random sampling algorithms
    • A. BUDHIRAJA AND H. J KUSHNER, Approximation and limit results for nonlinear filters over an infinite time interval. II. Random sampling algorithms, SIAM J. Control Optim., 38 (2000), pp. 1874-1908.
    • (2000) SIAM J. Control Optim. , vol.38 , pp. 1874-1908
    • Budhiraja, A.1    Kushner, H.J.2
  • 14
    • 0343826108 scopus 로고    scopus 로고
    • Long time behavior for some dynamical noise free nonlinear filtering problems
    • F. CEROU, Long time behavior for some dynamical noise free nonlinear filtering problems, SIAM J. Control Optim., 38 (2000), pp. 1086-1101.
    • (2000) SIAM J. Control Optim. , vol.38 , pp. 1086-1101
    • Cerou, F.1
  • 15
    • 0033313743 scopus 로고    scopus 로고
    • Relative entropy and error bounds for filtering of Markov process
    • J. M. C. CLARK, D. L. OCONE, AND C. COUMARBATCH, Relative entropy and error bounds for filtering of Markov process, Math. Control Signals Systems, 12 (1999), pp. 346-360.
    • (1999) Math. Control Signals Systems , vol.12 , pp. 346-360
    • Clark, J.M.C.1    Ocone, D.L.2    Coumarbatch, C.3
  • 16
    • 0033143342 scopus 로고    scopus 로고
    • Asymptotic ergodicity of the process of conditional law in some problem of non-linear filtering
    • G. DA PRATO, M. FUHRMAN, AND P. MALLIAVIN, Asymptotic ergodicity of the process of conditional law in some problem of non-linear filtering, J. Funct. Anal., 164 (1999), pp. 356-377.
    • (1999) J. Funct. Anal. , vol.164 , pp. 356-377
    • Prato, G.D.A.1    Fuhrman, M.2    Malliavin, P.3
  • 17
    • 0033196559 scopus 로고    scopus 로고
    • On the stability of measure valued processes with applications to filtering
    • P. DEL MORAL AND A. GUIONNET, On the stability of measure valued processes with applications to filtering, C. R. Acad. Sci. Paris Ser. I Math., 329 (1999), pp. 429-434.
    • (1999) C. R. Acad. Sci. Paris Ser. I Math. , vol.329 , pp. 429-434
    • Del Moral, P.1    Guionnet, A.2
  • 18
    • 0041332886 scopus 로고    scopus 로고
    • On the stability of interacting processes with applications to filtering and genetic algorithms
    • P. DEL MORAL AND A. GUIONNET, On the stability of interacting processes with applications to filtering and genetic algorithms, Ann. Inst. H. Poincaré Probab. Statist., 37 (2001), pp. 155-194.
    • (2001) Ann. Inst. H. Poincaré Probab. Statist. , vol.37 , pp. 155-194
    • Del Moral, P.1    Guionnet, A.2
  • 19
    • 0002210840 scopus 로고
    • Lyapunov exponents for filtering problem
    • M. H. A. Davis and R. J.Elliot, eds., Gordon & Breach, New York
    • B. DELYON AND O. ZEITOUNI, Lyapunov exponents for filtering problem, in Applied Stochastic Analysis, M. H. A. Davis and R. J.Elliot, eds., Gordon & Breach, New York, 1991, pp. 511-521.
    • (1991) Applied Stochastic Analysis , pp. 511-521
    • Delyon, B.1    Zeitouni, O.2
  • 22
    • 0001442283 scopus 로고
    • Asymptotic behavior of the nonlinear filtering errors of Markov processes
    • H. KUNITA, Asymptotic behavior of the nonlinear filtering errors of Markov processes, J. Multivariate Anal., 1 (1971), pp. 365-393.
    • (1971) J. Multivariate Anal. , vol.1 , pp. 365-393
    • Kunita, H.1
  • 23
    • 0003194655 scopus 로고
    • Ergodic properties of nonlinear filtering processes
    • Birkhäuser Boston, Boston
    • H. KUNITA, Ergodic properties of nonlinear filtering processes, in Spatial Stochastic Processes, Progr. Probab. 19, Birkhäuser Boston, Boston, 1991, pp. 233-256.
    • (1991) Spatial Stochastic Processes, Progr. Probab. , vol.19 , pp. 233-256
    • Kunita, H.1
  • 24
    • 0033889380 scopus 로고    scopus 로고
    • Exponential forgetting and geometric ergodicity in hidden Markov models
    • F. LE GLAND AND L. MEVEL, Exponential forgetting and geometric ergodicity in hidden Markov models, Math. Control Signals Systems, 13 (2000), pp. 63-93.
    • (2000) Math. Control Signals Systems , vol.13 , pp. 63-93
    • Le Gland, F.1    Mevel, L.2
  • 25
    • 16244373431 scopus 로고    scopus 로고
    • On the stability of nonlinear Feynman-Kac semigroups
    • P. DEL MORAL AND L. MICLO, On the stability of nonlinear Feynman-Kac semigroups, Ann. Fac. Sci. Toulouse Math.6, 11 (2002), pp. 135-175.
    • (2002) Ann. Fac. Sci. Toulouse Math.6 , vol.11 , pp. 135-175
    • Del Moral, P.1    Miclo, L.2
  • 28
    • 0034438096 scopus 로고    scopus 로고
    • Asymptotic optimality of approximate filters in stochastic systems with colored noises
    • A. LE BRETON AND M. ROUBAUD, Asymptotic optimality of approximate filters in stochastic systems with colored noises, SIAM J. Control Optim., 39 (2000), pp. 917-927.
    • (2000) SIAM J. Control Optim. , vol.39 , pp. 917-927
    • Le Breton, A.1    Roubaud, M.2
  • 32
    • 0001984607 scopus 로고
    • Filtering formula for partially observed linear systems with non-Gaussian initial conditions
    • A. M. MAKOWSKI, Filtering formula for partially observed linear systems with non-Gaussian initial conditions, Stochastics, 16 (1986), pp. 1-24.
    • (1986) Stochastics , vol.16 , pp. 1-24
    • Makowski, A.M.1
  • 33
    • 0026712610 scopus 로고
    • Discrete-time filtering for linear systems with non-Gaussian initial conditions: Asymptotic behaviors of the difference between the MMSE and the LMSE estimates
    • A. M. MAKOWSKI AND R. B. SOWERS, Discrete-time filtering for linear systems with non-Gaussian initial conditions: Asymptotic behaviors of the difference between the MMSE and the LMSE estimates, IEEE Trans. Automat. Control, 37 (1992), pp. 114-120.
    • (1992) IEEE Trans. Automat. Control , vol.37 , pp. 114-120
    • Makowski, A.M.1    Sowers, R.B.2
  • 34
    • 0003781238 scopus 로고    scopus 로고
    • Cambridge University Press, Cambridge, UK
    • J. R. NORRIS, Markov Chains, Cambridge University Press, Cambridge, UK, 1997.
    • (1997) Markov Chains
    • Norris, J.R.1
  • 35
    • 0029760763 scopus 로고    scopus 로고
    • Asymptotic stability of the optimal filter with respect to its initial condition
    • D. OCONE AND E. PARDOUX, Asymptotic stability of the optimal filter with respect to its initial condition, SIAM J. Control Optim., 34 (1996), pp. 226-243.
    • (1996) SIAM J. Control Optim. , vol.34 , pp. 226-243
    • Ocone, D.1    Pardoux, E.2
  • 36
    • 0033248040 scopus 로고    scopus 로고
    • Asymptotic stability of Beneš filters
    • D. OCONE, Asymptotic stability of Beneš filters, Stochastic Anal. Appl., 17 (1999), pp. 1053-1074.
    • (1999) Stochastic Anal. Appl. , vol.17 , pp. 1053-1074
    • Ocone, D.1
  • 39
    • 4344565347 scopus 로고
    • Kolmogorov's work on ergodic theory
    • YA. D. SINAI, Kolmogorov's work on ergodic theory, Ann. Probab., 17 (1989), pp. 833-839.
    • (1989) Ann. Probab. , vol.17 , pp. 833-839
    • Sinai, Ya.D.1
  • 40
    • 0000744184 scopus 로고
    • On invariant measure of filtering processes
    • Stochastic Differential Systems, Springer-Verlag, Berlin
    • L. STETTNER, On invariant measure of filtering processes, in Stochastic Differential Systems, Lecture Notes in Control and Inform. Sci. 126, Springer-Verlag, Berlin, 1989, pp. 279-292.
    • (1989) Lecture Notes in Control and Inform. Sci. , vol.126 , pp. 279-292
    • Stettner, L.1
  • 41
    • 0000936027 scopus 로고
    • Invariant measures of the pair: State, approximate filtering process
    • L. STETTNER, Invariant measures of the pair: State, approximate filtering process, Colloq. Math., 62 (1991), pp. 347-351.
    • (1991) Colloq. Math. , vol.62 , pp. 347-351
    • Stettner, L.1
  • 43
    • 0009295639 scopus 로고
    • Exchanging the order of taking suprema and countable intersections of σ-algebras
    • H. VON WEIZSÄCKER, Exchanging the order of taking suprema and countable intersections of σ-algebras, Ann. Inst. H. Poincaré Sect. B, 19 (1983), pp. 91-100.
    • (1983) Ann. Inst. H. Poincaré Sect. B , vol.19 , pp. 91-100
    • Von Weizsäcker, H.1
  • 45
    • 0001473054 scopus 로고
    • Some applications of stochastic differential equations to optimal nonlinear filtering
    • W. M. WONHAM, Some applications of stochastic differential equations to optimal nonlinear filtering, J. Soc. Indust. Appl. Math. Ser. A Control, 2 (1965), pp. 347-369.
    • (1965) J. Soc. Indust. Appl. Math. Ser. A Control , vol.2 , pp. 347-369
    • Wonham, W.M.1


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