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Volumn 31, Issue 2, 2003, Pages 693-718

Exact rates of convergence for a branching particle approximation to the solution of the Zakai equation

Author keywords

Branching algorithm; Filtering; Monte Carlo approximation; Particle filters; Zakai equation

Indexed keywords


EID: 0038336146     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/aop/1048516533     Document Type: Article
Times cited : (35)

References (20)
  • 3
    • 0001524126 scopus 로고    scopus 로고
    • Discrete filtering using branching and interacting particle systems
    • CRISAN, D., DEL MORAL, P. and LYONS, T. (1999). Discrete filtering using branching and interacting particle systems. Markov Process. Related Fields 5 293-318.
    • (1999) Markov Process. Related Fields , vol.5 , pp. 293-318
    • Crisan, D.1    Del Moral, P.2    Lyons, T.3
  • 4
    • 0032186558 scopus 로고    scopus 로고
    • Convergence of a branching particle method to the solution of the Zakai equation
    • CRISAN, D., GAINES, J. and LYONS, T. (1998). Convergence of a branching particle method to the solution of the Zakai equation. SIAM J. Appl. Probab. 58 1568-1591.
    • (1998) SIAM J. Appl. Probab. , vol.58 , pp. 1568-1591
    • Crisan, D.1    Gaines, J.2    Lyons, T.3
  • 5
    • 0031256242 scopus 로고    scopus 로고
    • Nonlinear filtering and measure valued processes
    • CRISAN, D. and LYONS, T. (1997). Nonlinear filtering and measure valued processes. Probab. Theory Related Fields 109 217-244.
    • (1997) Probab. Theory Related Fields , vol.109 , pp. 217-244
    • Crisan, D.1    Lyons, T.2
  • 6
    • 0033261066 scopus 로고    scopus 로고
    • A particle approximation of the solution of the Kushner-Stratonovitch equation
    • CRISAN, D. and LYONS, T. (1999). A particle approximation of the solution of the Kushner-Stratonovitch equation. Probab. Theory Related Fields 115 549-578.
    • (1999) Probab. Theory Related Fields , vol.115 , pp. 549-578
    • Crisan, D.1    Lyons, T.2
  • 9
    • 84972561398 scopus 로고
    • Stochastic differential equations for the non linear filtering problem
    • FUJISAKI, M., KALLIANPUR, G. and KUNITA, H. (1972). Stochastic differential equations for the non linear filtering problem. Osaka J. Math. 9 19-40.
    • (1972) Osaka J. Math. , vol.9 , pp. 19-40
    • Fujisaki, M.1    Kallianpur, G.2    Kunita, H.3
  • 10
    • 0001498426 scopus 로고
    • Estimation of stochastic systems: Arbitrary system process with additive white noise observation errors
    • KALLIANPUR, G. and STRIEBEL, C. (1968). Estimation of stochastic systems: Arbitrary system process with additive white noise observation errors. Ann. Math. Statist. 39 785-801
    • (1968) Ann. Math. Statist. , vol.39 , pp. 785-801
    • Kallianpur, G.1    Striebel, C.2
  • 13
    • 0001868645 scopus 로고
    • Unique characterisation of conditional distributions in nonlinear filtering
    • KURTZ, T. G. and OCONE, D. L. (1988). Unique characterisation of conditional distributions in nonlinear filtering. Ann. Probab. 16 80-107.
    • (1988) Ann. Probab. , vol.16 , pp. 80-107
    • Kurtz, T.G.1    Ocone, D.L.2
  • 14
    • 0000273833 scopus 로고    scopus 로고
    • Particle representation for a class of nonlinear SPDE's
    • KURTZ, T. G. and XIONG, J. (1999). Particle representation for a class of nonlinear SPDE's. Stochastic Process. Appl. 83 103-106.
    • (1999) Stochastic Process. Appl. , vol.83 , pp. 103-106
    • Kurtz, T.G.1    Xiong, J.2
  • 15
    • 0038772491 scopus 로고    scopus 로고
    • Numerical solutions for a class of SPDEs with application to filtering
    • T. Hida, R. L. Karandikar, H. Kunita, B. S. Rajput, S. Watanabe and J. Xiong, eds. Birkhäuser, Boston
    • KURTZ, T. G. and XIONG, J. (2001). Numerical solutions for a class of SPDEs with application to filtering. In Stochastics in Finite and Infinite Dimensions (T. Hida, R. L. Karandikar, H. Kunita, B. S. Rajput, S. Watanabe and J. Xiong, eds.) 233-258. Birkhäuser, Boston.
    • (2001) Stochastics in Finite and Infinite Dimensions , pp. 233-258
    • Kurtz, T.G.1    Xiong, J.2
  • 16
    • 0000272485 scopus 로고
    • Dynamical equations for optimal nonlinear filtering
    • KUSHNER, H. J. (1967). Dynamical equations for optimal nonlinear filtering. J. Differential Equations 3179-190.
    • (1967) J. Differential Equations , pp. 3179-3190
    • Kushner, H.J.1
  • 17
    • 0018768309 scopus 로고
    • Stochastic partial differential equations and filtering of diffusion processes
    • PARDOUX, E. (1979). Stochastic partial differential equations and filtering of diffusion processes. Stochastics 3 127-167.
    • (1979) Stochastics , vol.3 , pp. 127-167
    • Pardoux, E.1
  • 18
    • 0002064777 scopus 로고
    • Filtrage non linéaire et equations aux dérivées partielles stochastiques associées
    • Ecole d'Eté de Probabilités de Saint-Flour XIX. Springer, New York
    • PARDOUX, E. (1991). Filtrage non linéaire et equations aux dérivées partielles stochastiques associées. Ecole d'Eté de Probabilités de Saint-Flour XIX. Lecture Notes in Math. 1464. Springer, New York.
    • (1991) Lecture Notes in Math. , vol.1464
    • Pardoux, E.1
  • 19
    • 0009249278 scopus 로고
    • Sur les théories du filtrage et de la prédiction
    • Séminaire de Probabilités XI. Springer, New York
    • YOR, M. (1977). Sur les théories du filtrage et de la prédiction. Séminaire de Probabilités XI. Lecture Notes in Math. 581 257-297. Springer, New York.
    • (1977) Lecture Notes in Math. , vol.581 , pp. 257-297
    • Yor, M.1
  • 20
    • 0001702452 scopus 로고
    • On the optimal filtering of diffusion processes
    • ZAKAI, M. (1969). On the optimal filtering of diffusion processes. Z. Wahrsch. Verw. Gebiete 11 230-243.
    • (1969) Z. Wahrsch. Verw. Gebiete , vol.11 , pp. 230-243
    • Zakai, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.