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Volumn 21, Issue 5, 2003, Pages 995-1007

Maximum Likelihood Estimation in Partially Observed Stochastic Differential System Driven by a Fractional Brownian Motion

Author keywords

Asymptotic normality; Filtering; Fractional brownian motion; Long range dependence; Maximum likelihood estimate; Partially observed stochastic differential equations; Strong consistency

Indexed keywords


EID: 0141542556     PISSN: 07362994     EISSN: None     Source Type: Journal    
DOI: 10.1081/SAP-120024701     Document Type: Article
Times cited : (8)

References (37)
  • 2
  • 3
    • 38149048283 scopus 로고
    • MLE for partially observed diffusions: Direct maximization vs. the EM algorithm
    • Campillo, F.; Le Gland, F. MLE for partially observed diffusions: direct maximization vs. the EM algorithm. Stochastic Process Appl. 1989, 33, 245-274.
    • (1989) Stochastic Process Appl. , vol.33 , pp. 245-274
    • Campillo, F.1    Le Gland, F.2
  • 4
    • 84961469124 scopus 로고
    • Maximum likelihood estimation of a drift parameter from a partially observed diffusions in the case of small measurement noise
    • Konecky, F. Maximum likelihood estimation of a drift parameter from a partially observed diffusions in the case of small measurement noise. Statist. Decisions 1991, 8, 115-130.
    • (1991) Statist. Decisions , vol.8 , pp. 115-130
    • Konecky, F.1
  • 5
    • 0004839234 scopus 로고
    • Consistent parameter estimation for partially observed diffusions with small noise
    • James, M.; Le Gland, F. Consistent parameter estimation for partially observed diffusions with small noise. Applied Math. Optim. 1993, 32, 47-72.
    • (1993) Applied Math. Optim. , vol.32 , pp. 47-72
    • James, M.1    Le Gland, F.2
  • 6
    • 0141856381 scopus 로고
    • Parameter estimation for Kalman-Bucy filter with small noise
    • Kutoyants, Yu.A.; Pohlman, H. Parameter estimation for Kalman-Bucy filter with small noise. Statistics 1994, 25, 307-323.
    • (1994) Statistics , vol.25 , pp. 307-323
    • Kutoyants, Yu.A.1    Pohlman, H.2
  • 10
    • 0001187166 scopus 로고
    • Wiener skewline and other interesting curves in Hubert space
    • Kolmogorov, A.N. Wiener skewline and other interesting curves in Hubert space. Doklady Akad. Nauk 1940, 26, 115-118.
    • (1940) Doklady Akad. Nauk , vol.26 , pp. 115-118
    • Kolmogorov, A.N.1
  • 12
    • 0000501589 scopus 로고
    • Fractional Brownian motions, fractional noises and applications
    • Mandelbrot, B.; Van Ness, J.W. Fractional Brownian motions, fractional noises and applications. SIAM Rev. 1968, 10, 422-437.
    • (1968) SIAM Rev. , vol.10 , pp. 422-437
    • Mandelbrot, B.1    Van Ness, J.W.2
  • 13
    • 0038245992 scopus 로고
    • A New Method for Estimating the Parameter of Fractional Brownian Motion
    • Peltier, R.F.; Levy Vehel, J. A New Method for Estimating the Parameter of Fractional Brownian Motion, INRIA Research Report No. 2396; 1994.
    • (1994) INRIA Research Report No. 2396 , vol.2396
    • Peltier, R.F.1    Levy Vehel, J.2
  • 14
    • 0000746261 scopus 로고
    • Stochastic analysis of fractional Brownian motions
    • Lin, S.J. Stochastic analysis of fractional Brownian motions. Stochastics and Stochastics Reports 1995, 55, 121-140.
    • (1995) Stochastics and Stochastics Reports , vol.55 , pp. 121-140
    • Lin, S.J.1
  • 15
    • 53349108011 scopus 로고    scopus 로고
    • Itô formula with respect to fractional Brownian motion and its applications
    • Dai, W.; Heyde, C.C. Itô formula with respect to fractional Brownian motion and its applications. J. Appl. Math. Stoch. Anal. 1996, 9, 439-448.
    • (1996) J. Appl. Math. Stoch. Anal. , vol.9 , pp. 439-448
    • Dai, W.1    Heyde, C.C.2
  • 16
    • 0008562738 scopus 로고    scopus 로고
    • Existence and uniqueness theorem for fBm stochastic differential equations
    • Kleptsyna, M.L.; Kloeden, P.E.; Anh, V.V. Existence and uniqueness theorem for fBm stochastic differential equations. Problems of Information Transmission 1998, 34 (4), 51-61.
    • (1998) Problems of Information Transmission , vol.34 , Issue.4 , pp. 51-61
    • Kleptsyna, M.L.1    Kloeden, P.E.2    Anh, V.V.3
  • 18
    • 0042637937 scopus 로고    scopus 로고
    • Stochastic analysis of the fractional Brownian motion
    • Decreusefond, L.; Ustunel, A.S. Stochastic analysis of the fractional Brownian motion. Potential Anal. 1999, 10, 177-214.
    • (1999) Potential Anal. , vol.10 , pp. 177-214
    • Decreusefond, L.1    Ustunel, A.S.2
  • 19
    • 0033260473 scopus 로고    scopus 로고
    • Abstract nonlinear filtering in the presence of fractional Brownian motion
    • Coutin, L.; Decreusefond, L. Abstract nonlinear filtering in the presence of fractional Brownian motion. Ann. Appl. Probab. 1999, 9 (4), 1058-1090.
    • (1999) Ann. Appl. Probab. , vol.9 , Issue.4 , pp. 1058-1090
    • Coutin, L.1    Decreusefond, L.2
  • 21
    • 0000338690 scopus 로고    scopus 로고
    • Stochastic calculus with respect to fractional Brownian motion with Hurst parameter less than 1/2
    • Alos, E.; Mazet, O.; Nualart, D. Stochastic calculus with respect to fractional Brownian motion with Hurst parameter less than 1/2. Stoch. Proc. Appl. 2000, 86 (1), 121-139.
    • (2000) Stoch. Proc. Appl. , vol.86 , Issue.1 , pp. 121-139
    • Alos, E.1    Mazet, O.2    Nualart, D.3
  • 22
    • 0033878593 scopus 로고    scopus 로고
    • Stochastic calculus for fractional Brownian motion I
    • Duncan, T.E.; Hu, Y.; Pasik-Duncan, B. Stochastic calculus for fractional Brownian motion I. SIAM J. Control. Optim. 2000, 38, 582-612.
    • (2000) SIAM J. Control. Optim. , vol.38 , pp. 582-612
    • Duncan, T.E.1    Hu, Y.2    Pasik-Duncan, B.3
  • 23
    • 0038290919 scopus 로고    scopus 로고
    • Integration with respect to fractal functions and stochastic calculus
    • Zahle, M. Integration with respect to fractal functions and stochastic calculus. Prob. Theory. Rel. Filelds 1998, 111, 333-374.
    • (1998) Prob. Theory. Rel. Filelds , vol.111 , pp. 333-374
    • Zahle, M.1
  • 24
    • 0034258581 scopus 로고    scopus 로고
    • Stochastic integrals of Hölder continuous functions with respect to fractional Bronian motion
    • Ruzmaikina, A.A. Stochastic integrals of Hölder continuous functions with respect to fractional Bronian motion. J. Statistical Physics 2000, 100 (5&6), 1049-1069.
    • (2000) J. Statistical Physics , vol.100 , Issue.5-6 , pp. 1049-1069
    • Ruzmaikina, A.A.1
  • 25
    • 0000362483 scopus 로고
    • Decomposition of Dirichlet processes and its application
    • Lyons, T.J.; Zhang, T.S. Decomposition of Dirichlet processes and its application. Ann. Probab. 1994, 22, 494-524.
    • (1994) Ann. Probab. , vol.22 , pp. 494-524
    • Lyons, T.J.1    Zhang, T.S.2
  • 26
  • 28
    • 0032525495 scopus 로고    scopus 로고
    • Filtering and parameter estimation in a simple linear system driven by fractional Brownian motion
    • Le Breton, A. Filtering and parameter estimation in a simple linear system driven by fractional Brownian motion. Statist. Probab. Lett. 1998, 38, 263-274.
    • (1998) Statist. Probab. Lett. , vol.38 , pp. 263-274
    • Le Breton, A.1
  • 29
    • 0032041587 scopus 로고    scopus 로고
    • A Girsanov type approach to filtering in a simple linear system driven by fractional Brownian motion
    • Le Breton, A. A Girsanov type approach to filtering in a simple linear system driven by fractional Brownian motion. C. R. Acad. Sci. Paris, Series I 1998, 326, 997-1002.
    • (1998) C. R. Acad. Sci. Paris, Series I , vol.326 , pp. 997-1002
    • Le Breton, A.1
  • 30
    • 0141856378 scopus 로고    scopus 로고
    • An Elementary Approach to Filtering in Systems with Fractional Brownian Motion Observation Noise
    • Kleptsyna, M.L.; Le Breton, A.; Roubaud, M.C. An Elementary Approach to Filtering in Systems with Fractional Brownian Motion Observation Noise, INRIA Research Report No. 3439; 1998.
    • (1998) INRIA Research Report No. 3439 , vol.3439
    • Kleptsyna, M.L.1    Le Breton, A.2    Roubaud, M.C.3
  • 31
    • 0141856377 scopus 로고    scopus 로고
    • General approach to filtering with fractional Brownian noises-application to linear systems
    • Kleptsyna, M.L.; Le Breton, A.; Roubaud, M.C. General approach to filtering with fractional Brownian noises-application to linear systems. Stochastics and Stochastics Reports 2000, 71, 119-140.
    • (2000) Stochastics and Stochastics Reports , vol.71 , pp. 119-140
    • Kleptsyna, M.L.1    Le Breton, A.2    Roubaud, M.C.3
  • 32
    • 0001714525 scopus 로고    scopus 로고
    • An elementary approach to a Girsanov formula and other analytical results on fractional Brownian motion
    • Norros, I.; Valkeila, E.; Virtamo, J. An elementary approach to a Girsanov formula and other analytical results on fractional Brownian motion. Bernoulli 1999, 5, 571-587.
    • (1999) Bernoulli , vol.5 , pp. 571-587
    • Norros, I.1    Valkeila, E.2    Virtamo, J.3
  • 36
    • 0001399448 scopus 로고    scopus 로고
    • Long memory continuous time models
    • Comte, F.; Renault, E. Long memory continuous time models. J. Econometrics 1996, 73, 101-149.
    • (1996) J. Econometrics , vol.73 , pp. 101-149
    • Comte, F.1    Renault, E.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.