Linear stochastic equations in a Hilbert space with a fractional brownian motion

International Series in Operations Research and Management Science

Volumn 94, Issue , 2006, Pages 201-221

  Pasik Duncan, B ^a   Duncan, T E ^a   Maslowski, B ^b  

^a UNIVERSITY OF KANSAS   (United States)

^b INSTITUTE OF MATHEMATICS   (Czech Republic)

Author keywords

Fractional Brownian motion; Linear stochastic equations in Hilbert space; Ornstein Uhlenbeck processes; Sample path properties of solutions; Stochastic linear partial differential equations

Indexed keywords

EID: 84903984447     PISSN: 08848289     EISSN: None     Source Type: Book Series    
DOI: None     Document Type: Chapter

References (18)

1. E. Alòs, O. Mazet, and D. Nualart. Stochastic calculus with respect to Gaussian processes. Ann. Probab., 29(2):766-801, 2001.
2. P. Caithamer. The stochastic wave equation driven by fractional Brownian noise and temporally correlated smooth noise. Stoch. Dyn., 5(1):45-64, 2005.
3. T. E. Duncan, J. Jakubowski, and B. Pasik-Duncan. Stochastic integration for fraction Brownian motion in a Hilbert space. To appear in Stochastic Dynamics.
4. T. E. Duncan, B. Maslowski, and B. Pasik-Duncan. Stochastic equations in Hilbert space with a multiplicative fractional Gaussian noise. Stoc. Proc. Appl., 115:1357-1383, 2005.
5. T. E. Duncan, B. Pasik-Duncan, and B. Maslowski. Frac tional Brownian motion and stochastic equations in Hilbert spaces. Stoch. Dyn., 2(2):225-250, 2002.
6. G. Da Prato and J. Zabczyk. Stochastic equations in infinite dimensions, volume 44 of Encyclopedia of Mathematics and its Applications. Cambridge University Press, Cambridge, 1992.
7. G. Da Prato and J. Zabczyk. Ergodicity for infinite-dimensional systems, volume 229 of London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge, 1996.
8. L. Decreusefond and A. S. Üstünel. Stochastic analysis of the fractional Brownian motion. Potential Anal., 10(2):177-214, 1999.
9. T. E. Duncan. Some stochastic semilinear equations in Hilbert space with fractional Brownian motion. In J. Menaldi, E. Rofman, and A Sulem, editors, Optimal Control and Partial Differential Equations, pages 241-247. IOS Press, Amsterdam, 2000.
10. W. Grecksch and V. V. Anh. A parabolic stochastic differential equation with fractional Brownian motion input. Statist. Probab. Lett., 41(4):337-346, 1999.
11. Y. Hu, B. Øksendal, and T. Zhang. General fractional multiparameter white noise theory and stochastic partial differential equations. Comm. Partial Differential Equations, 29(1-2):1-23, 2004.
12. Y. Hu. Heat equations with fractional white noise potentials. Appl. Math. Optim., 43(3):221-243, 2001.
13. Y. Hu. Integral transformations and anticipative calculus for fractional Brownian motions. Mem. Amer. Math. Soc., 175(825):viii+127, 2005.
14. S. Moret and D. Nualart. Onsager-Machlup functional for the fractional Brownian motion. Probab. Theory Related Fields, 124(2):227-260, 2002.
15. B. Maslowski and B. Schmalfuss. Random dynamical systems and stationary solutions of differential equations driven by the fractional Brownian motion. Stochastic Anal. Appl., 22(6):1577-1607, 2004.
16. V. Pipiras and M. S. Taqqu. Integration questions related to fractional Brownian motion. Probab. Theory Related Fields, 118(2):251-291, 2000.
17. S. G. Samko, A. A. Kilbas, and O. I. Marichev. Fractional integrals and derivatives. Gordon and Breach Science Publishers, Yverdon, 1993. Theory and applications.
18. S. Tindel, C. A. Tudor, and F. Viens. Stochastic evolution equations with fractional Brownian motion. Probab. Theory Related Fields, 127(2):186-204, 2003.