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Volumn 23, Issue 1, 2005, Pages 55-67

Nonlinear filtering with fractional Brownian motion noise

Author keywords

Fractional Brownian motions; Kushner FKK equation; Martingale problem; Nonlinear filtering; Zakai equation

Indexed keywords


EID: 15244356933     PISSN: 07362994     EISSN: None     Source Type: Journal    
DOI: 10.1081/SAP-200044429     Document Type: Article
Times cited : (10)

References (19)
  • 3
    • 21344437201 scopus 로고
    • Uniqueness and robustness of solution of measure-valued equations of nonlinear filtering
    • Bhatt, A.G., G. Kallianpur, and R.L. Karandikar. 1995. Uniqueness and robustness of solution of measure-valued equations of nonlinear filtering. Ann. Probab. 23(4): 1895-1938.
    • (1995) Ann. Probab. , vol.23 , Issue.4 , pp. 1895-1938
    • Bhatt, A.G.1    Kallianpur, G.2    Karandikar, R.L.3
  • 4
    • 0033260473 scopus 로고    scopus 로고
    • Abstract nonlinear filtering theory in the presence of fractional Brownian motion
    • Coutin, L., and L. Decreusefond. 1999. Abstract nonlinear filtering theory in the presence of fractional Brownian motion. Ann. Appl. Probab. 9(4): 1058-1090.
    • (1999) Ann. Appl. Probab. , vol.9 , Issue.4 , pp. 1058-1090
    • Coutin, L.1    Decreusefond, L.2
  • 5
    • 84972561398 scopus 로고
    • Stochastic differential equation for the nonlinar filtering problem
    • Fujisaki, M., G. Kallianpur, and H. Kunita. 1972. Stochastic differential equation for the nonlinar 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
  • 7
    • 0001659363 scopus 로고
    • Convergence in distribution of conditional expectations
    • Goggin, E.M. 1994. Convergence in distribution of conditional expectations. Ann. Probab. 22(2): 1097-1114.
    • (1994) Ann. Probab. , vol.22 , Issue.2 , pp. 1097-1114
    • Goggin, E.M.1
  • 10
    • 0141878232 scopus 로고    scopus 로고
    • Linear filtering with fractional Brownian motion in the signal and observation processes
    • Kleptsyna, M.L., P.E. Kloeden, and V.V. Anh. 1999. Linear filtering with fractional Brownian motion in the signal and observation processes. J. Appl. Math. Stochastic Anal. 12(1):85-90.
    • (1999) J. Appl. Math. Stochastic Anal. , vol.12 , Issue.1 , pp. 85-90
    • Kleptsyna, M.L.1    Kloeden, P.E.2    Anh, V.V.3
  • 11
    • 0032392894 scopus 로고    scopus 로고
    • Nonlinear filtering with fractional Brownian motion
    • Kleptsyna, M.L., P.E. Kloeden, and V.V. Anh. 1998. Nonlinear filtering with fractional Brownian motion. Stochastic Anal. Appl. 16(5):907-914.
    • (1998) Stochastic Anal. Appl. , vol.16 , Issue.5 , pp. 907-914
    • Kleptsyna, M.L.1    Kloeden, P.E.2    Anh, V.V.3
  • 12
    • 15244345021 scopus 로고    scopus 로고
    • Extension of the Kalman-Bucy filter to elementary linear systems with fractional Brownian noises
    • Kleptsyna, M.L., and A. Le Breton. 2002. Extension of the Kalman-Bucy filter to elementary linear systems with fractional Brownian noises. Stat. Inference Stoch. Process. 5(3):249-271.
    • (2002) Stat. Inference Stoch. Process. , vol.5 , Issue.3 , pp. 249-271
    • Kleptsyna, M.L.1    Le Breton, A.2
  • 13
    • 0141856377 scopus 로고    scopus 로고
    • General approach to filtering with fractional Brownian noises:Application to linear systems
    • Kleptsyna, M.L., A. Le Breton, and M.C. Roubaud. 2000. General approach to filtering with fractional Brownian noises:Application to linear systems. Stochastics Stochastics Rep. 71(1-2): 119-140.
    • (2000) Stochastics Stochastics Rep. , vol.71 , Issue.1-2 , pp. 119-140
    • Kleptsyna, M.L.1    Le Breton, A.2    Roubaud, M.C.3
  • 14
    • 0000367265 scopus 로고
    • Weak limit theorems for stochastic integrals and stochastic differential equations
    • Kurtz, T.G., and P. Protter. 1991. Weak limit theorems for stochastic integrals and stochastic differential equations. Ann. Probab. 19(3): 1035-1070.
    • (1991) Ann. Probab. , vol.19 , Issue.3 , pp. 1035-1070
    • Kurtz, T.G.1    Protter, P.2
  • 15
    • 33746292669 scopus 로고
    • Dynamical equation for optimal nonlinear filtering
    • Kushner, H. 1967. Dynamical equation for optimal nonlinear filtering. J. Differential Equations 3:179-190.
    • (1967) J. Differential Equations , vol.3 , pp. 179-190
    • Kushner, H.1
  • 16
    • 0032525495 scopus 로고    scopus 로고
    • Filtering and parameter estimation in a simple linear system driven by a fractional Brownian motion
    • Le Breton, A. 1998. Filtering and parameter estimation in a simple linear system driven by a fractional Brownian motion. Statistics and Probability Letters 38:263-274.
    • (1998) Statistics and Probability Letters , vol.38 , pp. 263-274
    • Le Breton, A.1
  • 17
    • 0034438181 scopus 로고    scopus 로고
    • A Bayes formula for Gaussian noise processes and its applications
    • Mandal, P. K., and V. Mandrekar. 2000. A Bayes formula for Gaussian noise processes and its applications. SIAM J. Control Optim. 39(3):852-871.
    • (2000) SIAM J. Control Optim. , vol.39 , Issue.3 , pp. 852-871
    • Mandal, P.K.1    Mandrekar, V.2
  • 18
    • 0001714525 scopus 로고    scopus 로고
    • An elementary approach to a Girsanov formula and other analytical results on fractional Brownian motions
    • Norros, I., E. Valkeila, and J. Virtamo. 1999. An elementary approach to a Girsanov formula and other analytical results on fractional Brownian motions. Brenoulli 5:571-587.
    • (1999) Brenoulli , vol.5 , pp. 571-587
    • Norros, I.1    Valkeila, E.2    Virtamo, J.3
  • 19
    • 0001702452 scopus 로고
    • On the optimal filtering of diffusion process
    • Zakai, M. 1969. On the optimal filtering of diffusion process. 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.