Free Access
Issue
ESAIM: PS
Volume 12, April 2008
Page(s) 94 - 126
DOI https://doi.org/10.1051/ps:2007046
Published online 23 January 2008
  1. F. Biagini, Y. Hu, B. Øksendal, and A. Sulem, A stochastic maximum principle for processes driven by fractional Brownian motion. Stoch. Processes Appl. 100 (2002) 233–253. [CrossRef]
  2. H. Cramer and M.R. Leadbetter, Stationary and related stochastic processes. John Wiley & Sons, Inc. (1967).
  3. M.H.A. Davis, Linear Estimation and Stochastic Control. Chapman and Hall (1977).
  4. L. Decreusefond and A.S. Üstünel, Stochastic analysis of the fractional Brownian motion. Potential Analysis 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. Prob. 33 (1996) 400–410. [CrossRef] [MathSciNet]
  7. M.L. Kleptsyna and A. Le Breton, Statistical analysis of the fractional Ornstein-Uhlenbeck type process. Stat. Inf. Stoch. 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. Stat. Inf. Stoch. 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. Stoch. Stoch. 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. Stat. Oper. Res. Trans. 28 (2004) 177–190.
  12. M.L. Kleptsyna, A. Le Breton and M. Viot, On the infinite time horizon linear-quadratic regulator problem under a fractional Brownian perturbation. ESAIM: PS 9 (2005) 185–205. [CrossRef] [EDP Sciences]
  13. R.S. Liptser and A.N. Shiryaev, Statistics of Random Processes. Springer-Verlag (1978).
  14. R.S. Liptser and A.N. Shiryaev, Theory of Martingales. Kluwer Academic Publ., Dordrecht (1989).
  15. 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]
  16. 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]
  17. W.M. Wonham, On the separation principle of stochastic control. SIAM J. Control 6 (1968) 312–326. [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.