Free Access
Issue
ESAIM: PS
Volume 9, June 2005
Page(s) 185 - 205
DOI https://doi.org/10.1051/ps:2005008
Published online 15 November 2005
  1. F. Biaggini, Y. Hu, B. Øksendal and A. Sulem, A stochastic maximum principle for processes driven by fractional Brownian motion. Stochastic Processes Appl. 100 (2002) 233–253. [CrossRef]
  2. D. Blackwell and L. Dubins, Merging of opinions with increasing information. Ann. Math. Statist. 33 (1962) 882–886. [CrossRef] [MathSciNet]
  3. M.H.A. Davis, Linear Estimation and Stochastic Control. Chapman and Hall, New York (1977).
  4. L. Decreusefond and A.S. Üstünel, Stochastic analysis of the fractional Brownian motion. Potential Anal. 10 (1999) 177–214. [CrossRef] [MathSciNet]
  5. T.E. Duncan, Y. Hu and B. Pasik-Duncan, Stochastic calculus for fractional Brownian motion I. Theory. SIAM J. Control Optim. 38 (2000) 582–612. [CrossRef] [MathSciNet]
  6. G. Gripenberg and I. Norros, On the prediction of fractional Brownian motion. J. Appl. Probab. 33 (1996) 400–410. [CrossRef] [MathSciNet]
  7. M.L. Kleptsyna and A. Le Breton, Statistical analysis of the fractional Ornstein-Uhlenbeck type process. Statist. Inference Stochastic Processes 5 (2002) 229–248. [CrossRef]
  8. M.L. Kleptsyna and A. Le Breton, Extension of the Kalman-Bucy filter to elementary linear systems with fractional Brownian noises. Statist. Inference Stochastic Processes 5 (2002) 249–271. [CrossRef]
  9. M.L. Kleptsyna, A. Le Breton and M.-C. Roubaud, General approach to filtering with fractional Brownian noises – Application to linear systems. Stochastics Reports 71 (2000) 119–140.
  10. M.L. Kleptsyna, A. Le Breton and M. Viot, About the linear-quadratic regulator problem under a fractional Brownian perturbation. ESAIM: PS 7 (2003) 161–170. [CrossRef] [EDP Sciences]
  11. M.L. Kleptsyna, A. Le Breton and M. Viot, Asymptotically optimal filtering in linear systems with fractional Brownian noises. Statist. Oper. Res. Trans. (2004) 28 177–190.
  12. A. Le Breton, Adaptive control in the scalar linear-quadratic model in continious time. Statist. Probab. Lett. 13 (1992) 169–177. [CrossRef] [MathSciNet]
  13. R.S. Liptser and A.N. Shiryaev, Statist. Random Processes. Springer-Verlag, New York (1978).
  14. R.S. Liptser and A.N. Shiryaev, Theory of Martingales. Kluwer Academic Publ., Dordrecht (1989).
  15. G.M. Molchan, Linear problems for fractional Brownian motion: group approach. Probab. Theory Appl. 1 (2002) 59–70 (in Russian).
  16. G.M. Molchan, Gaussian processes with spectra which are asymptotically equivalent to a power of λ. Probab. Theory Appl. 14 (1969) 530–532. [CrossRef]
  17. G.M. Molchan and J.I. Golosov, Gaussian stationary processes with which are asymptotic power spectrum. Soviet Math. Dokl. 10 (1969) 134–137.
  18. I. Norros, E. Valkeila and J. Virtamo, An elementary approach to a Girsanov formula and other analytical results on fractional Brownian motions. Bernoulli 5 (1999) 571–587. [CrossRef] [MathSciNet]
  19. C.J. Nuzman and H.V. Poor, Linear estimation of self-similar processes via Lamperti's transformation. J. Appl. Prob. 37 (2000) 429–452. [CrossRef] [MathSciNet]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.