Volume 15, 2011
|Page(s)||110 - 138|
|Published online||05 January 2012|
- E. Alòs, O. Mazet and D. Nualart, Stochastic calculus with respect to Gaussian processes. Ann. Probab. 29 (2001) 766–801. [CrossRef] [MathSciNet]
- E. Alòs and D. Nualart, Stochastic integration with respect to the fractional Brownian motion. Stoch. Stoch. Rep. 75 (2003) 129–152. [CrossRef] [MathSciNet]
- 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.
- P. Carmona and L. Coutin, Stochastic integration with respect to fractional Brownian motion. Ann. Inst. Poincaré, Probab. & Stat. 39 (2003) 27–68.
- G. Da Prato and J. Zabczyk, Stochastic Equations in Infinite Dimensions. Cambridge University Press (1992).
- L. Decreusefond and A.S. Ustünel, Stochastic analysis of the fractional Brownian motion. Potent. Anal. 10 (1999) 177–214. [CrossRef] [MathSciNet]
- 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]
- W. Grecksch and V.V. Anh, A parabolic stochastic differential equation with fractional Brownian motion input. Stat. Probab. Lett. 41 (1999) 337–346. [NASA ADS] [CrossRef] [MathSciNet] [PubMed]
- Y. Hu, Integral transformations and anticipative calculus for fractional Brownian motions. Memoirs AMS 175 (2005) viii+127.
- G. Kallianpur and J. Xiong, Stochastic Differential Equations in Infinite Dimensional Spaces. IMS Lect. Notes 26, Hayward, CA (1995).
- 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]
- 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]
- 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]
- 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.
- T. Lyons, Differential equations driven by rough signals. Rev. Mat. Iberoamericana 14 (1998) 215–310. [CrossRef] [MathSciNet]
- T. Lyons and Z. Qian, System Control and Rough Paths. Oxford University Press (2002).
- B. Maslowski and D. Nualart, Evolution equations driven by a fractional Brownian motion. J. Funct. Anal. 202 (2003) 277–305. [CrossRef] [MathSciNet]
- D. Nualart, Analysis on Wiener space and anticipative stochastic calculus. Lect. Notes. Math. 1690 (1998) 123–227. [CrossRef]
- D. Nualart, Stochastic integration with respect to fractional Brownian motion and applications. Contem. Math. 336 (2003) 3–39. [CrossRef]
- D. Nualart, Malliavin Calculus and Related Topics, Second Edition. Springer-Verlag, Berlin.
- 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]
- B.L. Rozovskii, Stochastic evolution systems. Kluwer, Dordrecht (1990).
- 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
- E.M. Stein, Singular Integrals and Differentiability Properties of Functions. Princeton University Press, Princeton (1970).
- S. Tindel, C.A. Tudor, and F. Viens, Stochastic evolution equations with fractional Brownian motion. Probab. Th. Rel. Fields 127 (2003) 186–204. [CrossRef]
- 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]
- M. Zähle, Integration with respect to fractal functions and stochastic calculus I. Probab. Th. Rel. Fields 111 (1998) 333–374. [CrossRef]
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.