Optimal Control for Non-Homogeneous Linear Systems Driven by Fractional Noises

References

• Carmona , P. , and Coutin , L. 2003 . Stochastic integration with respect to fractional Brownian motion . Annals of Institute of Henri Poincarè 39 : 27 – 68 .
   Web of Science ®Google Scholar
• Duncan , T.E. , Hu , Y. , Pasik-Duncan , B. 2000 . Stochastic calculus for fractional Brownian motion I. Theory . SIAM Journal of Control Optimization 38 ( 2 ): 582 – 612 .
   Web of Science ®Google Scholar
• Elliott , R.J. , and Van Der Hoek , J. 2003 . A general fractional white noise theory and applications to finance . Mathematical Finance 13 : 301 – 330 .
   Web of Science ®Google Scholar
• Hu , Y. , and Zhou , X.Y. , 2005 . Stochastic control for linear systems driven by fractional noises . SIAM Journal of Control Optimization 43 ( 6 ): 2245 – 2277 .
   Web of Science ®Google Scholar
• Hu , Y. , and Øksendal , B. , 2003 . Fractional white noise calculus and applications to Finance . Infinite Dimensional Analysis and Quantum Probability and Related Topics 6 : 1 – 32 .
   Web of Science ®Google Scholar
• Hurst , H.E. 1951 . Long-term capacity in reservoirs . Transactions of the American Society of Civil Engineers 116 : 400 – 410 .
   Google Scholar
• Kleptsyna , M.L. , Le Breton , A. , and Viot , M. 2003 . About the linear-quadratic regulator problem under a fractional Brownian perturbation . ESAIM Probability Statistics 7 : 161 – 170 .
   Google Scholar
• Malliavin , P. 1978. Stochastic calculus of variations and hypoelliptic operators. Proceedings of the International Symposiumon on Stochastic Differential Equations (Kyoto-1976), Wiley , New York, 195–263.
   Google Scholar
• Mandelbrot , B.B. , and Van Ness , J.W. 1968 . Fractional Brownian motions, fractional Brownian noises and applications . SIAM Review 10 : 422 – 437 .
   Web of Science ®Google Scholar
• Norros , I. , Valkeila , E. , and Virtamo , J. 1999 . An elementary approach to a Girsanov formula and other analytical results on fractional Brownian motions . Bernoulli 5 ( 4 ): 571 – 587 .
   Web of Science ®Google Scholar
• Nualart , D. , 2006 . Fractional Brownian motion: Stochastic calculus and applications . Proceedings of the International Congress of Mathematicians, Madrid, Spain , 3 : 1541 – 1562 .
   Google Scholar