On the infinite time horizon linear-quadratic regulator problem under a fractional brownian perturbation

 Access to full text

 Full (PDF)

1. [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. Zbl1064.93048
2. [2] D. Blackwell and L. Dubins, Merging of opinions with increasing information. Ann. Math. Statist. 33 (1962) 882–886. Zbl0109.35704
3. [3] M.H.A. Davis, Linear Estimation and Stochastic Control. Chapman and Hall, New York (1977). Zbl0437.60001MR476099
4. [4] L. Decreusefond and A.S. Üstünel, Stochastic analysis of the fractional Brownian motion. Potential Anal. 10 (1999) 177–214. Zbl0924.60034
5. [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. Zbl0947.60061
6. [6] G. Gripenberg and I. Norros, On the prediction of fractional Brownian motion. J. Appl. Probab. 33 (1996) 400–410. Zbl0861.60049
7. [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. Zbl1021.62061
8. [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. Zbl1011.60018
9. [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. Zbl0979.93117
10. [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. Zbl1030.93059
11. [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. Zbl1274.60117
12. [12] A. Le Breton, Adaptive control in the scalar linear-quadratic model in continious time. Statist. Probab. Lett. 13 (1992) 169–177. Zbl0744.93090
13. [13] R.S. Liptser and A.N. Shiryaev, Statist. Random Processes. Springer-Verlag, New York (1978). 
14. [14] R.S. Liptser and A.N. Shiryaev, Theory of Martingales. Kluwer Academic Publ., Dordrecht (1989). Zbl0728.60048MR1022664
15. [15] G.M. Molchan, Linear problems for fractional Brownian motion: group approach. Probab. Theory Appl. 1 (2002) 59–70 (in Russian). Zbl1035.60084
16. [16] G.M. Molchan, Gaussian processes with spectra which are asymptotically equivalent to a power of $\lambda$. Probab. Theory Appl. 14 (1969) 530–532. 
17. [17] G.M. Molchan and J.I. Golosov, Gaussian stationary processes with which are asymptotic power spectrum. Soviet Math. Dokl. 10 (1969) 134–137. Zbl0181.20704
18. [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. Zbl0955.60034
19. [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. Zbl0963.60034

1. Marina L. Kleptsyna, Alain Le Breton, Michel Viot, Separation principle in the fractional Gaussian linear-quadratic regulator problem with partial observation