Free Access
Issue
ESAIM: PS
Volume 15, 2011
Page(s) 110 - 138
DOI https://doi.org/10.1051/ps/2009006
Published online 05 January 2012
  1. E. Alòs, O. Mazet and D. Nualart, Stochastic calculus with respect to Gaussian processes. Ann. Probab. 29 (2001) 766–801. [CrossRef] [MathSciNet] [Google Scholar]
  2. E. Alòs and D. Nualart, Stochastic integration with respect to the fractional Brownian motion. Stoch. Stoch. Rep. 75 (2003) 129–152. [CrossRef] [MathSciNet] [Google Scholar]
  3. R.M. Balan and C.A. Tudor, The stochastic heat equation with a fractional-colored noise: existence of the solution. Latin Amer. J. Probab. Math. Stat. 4 (2008) 57–87. [Google Scholar]
  4. P. Carmona and L. Coutin, Stochastic integration with respect to fractional Brownian motion. Ann. Inst. Poincaré, Probab. & Stat. 39 (2003) 27–68. [Google Scholar]
  5. G. Da Prato and J. Zabczyk, Stochastic Equations in Infinite Dimensions. Cambridge University Press (1992). [Google Scholar]
  6. L. Decreusefond and A.S. Ustünel, Stochastic analysis of the fractional Brownian motion. Potent. Anal. 10 (1999) 177–214. [Google Scholar]
  7. T.E. Duncan, Y. Hu and B. Pasik-Duncan, Stochstic calculus for fractional Brownian motion I. theory. SIAM J. Contr. Optim. 38 (2000) 582–612. [CrossRef] [MathSciNet] [Google Scholar]
  8. W. Grecksch and V.V. Anh, A parabolic stochastic differential equation with fractional Brownian motion input. Stat. Probab. Lett. 41 (1999) 337–346. [Google Scholar]
  9. Y. Hu, Integral transformations and anticipative calculus for fractional Brownian motions. Memoirs AMS 175 (2005) viii+127. [Google Scholar]
  10. G. Kallianpur and J. Xiong, Stochastic Differential Equations in Infinite Dimensional Spaces. IMS Lect. Notes 26, Hayward, CA (1995). [Google Scholar]
  11. N.V. Krylov, A generalization of the Littlewood-Paley inequality and some other results related to stochstic partial differential equations. Ulam Quarterly 2 (1994) 16–26. [MathSciNet] [Google Scholar]
  12. N.V. Krylov, On Lp-theory of stochastic partial differential equations in the whole space. SIAM J. Math. Anal. 27 (1996) 313–340 [CrossRef] [MathSciNet] [Google Scholar]
  13. N.V. Krylov, An analytic approach to SPDEs. In Stochastic partial differential equations: six perspectives. Math. Surveys Monogr. 64 (1999) 185–242 AMS, Providence, RI. [CrossRef] [Google Scholar]
  14. N.V. Krylov, On the foundation of the L p-theory of stochastic partial differential equations. In “Stochastic partial differential equations and application VII”. Chapman & Hall, CRC (2006) 179–191. [Google Scholar]
  15. T. Lyons, Differential equations driven by rough signals. Rev. Mat. Iberoamericana 14 (1998) 215–310. [CrossRef] [MathSciNet] [Google Scholar]
  16. T. Lyons and Z. Qian, System Control and Rough Paths. Oxford University Press (2002). [Google Scholar]
  17. B. Maslowski and D. Nualart, Evolution equations driven by a fractional Brownian motion. J. Funct. Anal. 202 (2003) 277–305. [CrossRef] [MathSciNet] [Google Scholar]
  18. D. Nualart, Analysis on Wiener space and anticipative stochastic calculus. Lect. Notes. Math. 1690 (1998) 123–227. [CrossRef] [Google Scholar]
  19. D. Nualart, Stochastic integration with respect to fractional Brownian motion and applications. Contem. Math. 336 (2003) 3–39. [CrossRef] [Google Scholar]
  20. D. Nualart, Malliavin Calculus and Related Topics, Second Edition. Springer-Verlag, Berlin. [Google Scholar]
  21. D. Nualart and P.-A. Vuillermot, Variational solutions for partial differential equations driven by fractional a noise. J. Funct. Anal. 232 (2006) 390–454. [CrossRef] [MathSciNet] [Google Scholar]
  22. B.L. Rozovskii, Stochastic evolution systems. Kluwer, Dordrecht (1990). [Google Scholar]
  23. M. Sanz-Solé and P.-A. Vuillermot, Mild solutions for a class of fractional SPDE's and their sample paths (2007). Preprint available at http://www.arxiv.org/pdf/0710.5485 [Google Scholar]
  24. E.M. Stein, Singular Integrals and Differentiability Properties of Functions. Princeton University Press, Princeton (1970). [Google Scholar]
  25. S. Tindel, C.A. Tudor, and F. Viens, Stochastic evolution equations with fractional Brownian motion. Probab. Th. Rel. Fields 127 (2003) 186–204. [Google Scholar]
  26. J.B. Walsh, An introduction to stochastic partial differential equations. École d'Été de Probabilités de Saint-Flour XIV. Lecture Notes in Math. 1180 (1986) 265–439. Springer, Berlin. [CrossRef] [Google Scholar]
  27. M. Zähle, Integration with respect to fractal functions and stochastic calculus I. Probab. Th. Rel. Fields 111 (1998) 333–374. [CrossRef] [Google Scholar]

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