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Original Articles

Nonlinear Filtering with Fractional Brownian Motion Noise

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Pages 55-67 | Received 12 Jun 2003, Accepted 31 Mar 2004, Published online: 01 Sep 2006

REFERENCES

  • Amirdjanova , A. 2002 . Nonlinear filtering with fractional Brownian motion . Special issue dedicated to the memory of Jacques-Louis Lions Appl. Math. Optim. 46 ( 2-3 ): 81 – 88 .
  • Barton , R. J. , and H. V. Poor . 1988 . Signal detection in fractional Gaussian noise . IEEE Transactions on Information Theory 34 ( 5 ): 943 – 959 . [CSA] [CROSSREF]
  • 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 .
  • Coutin , L. , and L. Decreusefond . 1999 . Abstract nonlinear filtering theory in the presence of fractional Brownian motion . Ann. Appl. Probab. 9 ( 4 ): 1058 – 1090 . [CROSSREF]
  • Fujisaki , M. , G. Kallianpur , and H. Kunita . 1972 . Stochastic differential equation for the nonlinar filtering problem . Osaka J. Math. 9 : 19 – 40 .
  • Gawarecki , L. , and V. Mandrekar . 2001 . On the Zakai equation of filtering with Gaussian noise . In Stochastics in Finite and Infinite Dimensions , [ 145 – 151 ]. Boston , MA : Birkhuser .
  • Goggin , E. M. 1994 . Convergence in distribution of conditional expectations . Ann. Probab . 22 ( 2 ): 1097 – 1114 .
  • Ikeda , N. , and S. Watanabe . 1981 . In Stochastic Differential Equations and Diffusion Processes . Amsterdam : North-Holland publishing Company .
  • Kallianpur , G. 1980 . Stochastic Filtering Theory . New York–Berlin Springer-Verlag .
  • 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 .
  • Kleptsyna , M. L. , P. E. Kloeden , and V. V. Anh . 1998 . Nonlinear filtering with fractional Brownian motion . Stochastic Anal. Appl. 16 ( 5 ): 907 – 914 .
  • 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 . [CROSSREF]
  • 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 .
  • Kurtz , T. G. , and P. Protter 1991 . Weak limit theorems for stochastic integrals and stochastic differential equations . Ann. Probab. 19 ( 3 ): 1035 – 1070 .
  • Kushner , H. 1967 . Dynamical equation for optimal nonlinear filtering . J. Differential Equations 3 : 179 – 190 . [CROSSREF]
  • 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. [CROSSREF]
  • 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 . [CROSSREF]
  • 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 .
  • Zakai , M. 1969 . On the optimal filtering of diffusion process . Z. Wahrsch. Verw. Gebiete 11 : 230 – 243 . [CROSSREF]

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