The PDF file you selected should load here if your Web browser has a PDF reader plug-in installed (for example, a recent version of Adobe Acrobat Reader).

Alternatively, you can also download the PDF file directly to your computer, from where it can be opened using a PDF reader. To download the PDF, click the Download link below.

If you would like more information about how to print, save, and work with PDFs, Highwire Press provides a helpful Frequently Asked Questions about PDFs.

Download this PDF file Fullscreen Fullscreen Off

References

  1. Brzeźniak, Zdzisław. On stochastic convolution in Banach spaces and applications. Stochastics Stochastics Rep. 61 (1997), no. 3-4, 245--295. MR1488138
  2. Caruana, Michael; Friz, Peter. Partial differential equations driven by rough paths. J. Differential Equations 247 (2009), no. 1, 140--173. MR2510132 (2010g:60149)
  3. Caruana, Michael; Friz, Peter K.; Oberhauser, Harald. A (rough) pathwise approach to a class of non-linear stochastic partial differential equations. Ann. Inst. H. Poincaré Anal. Non Linéaire 28 (2011), no. 1, 27--46. MR2765508
  4. Coutin, Laure; Qian, Zhongmin. Stochastic analysis, rough path analysis and fractional Brownian motions. Probab. Theory Related Fields 122 (2002), no. 1, 108--140. MR1883719 (2003c:60066)
  5. Da Prato, Giuseppe; Zabczyk, Jerzy. Stochastic equations in infinite dimensions.Encyclopedia of Mathematics and its Applications, 44. Cambridge University Press, Cambridge, 1992. xviii+454 pp. ISBN: 0-521-38529-6 MR1207136 (95g:60073)
  6. Davie, A. M. Differential equations driven by rough paths: an approach via discrete approximation. Appl. Math. Res. Express. AMRX 2007, no. 2, Art. ID abm009, 40 pp. MR2387018 (2009e:34172)
  7. Davies, E. B. Heat kernels and spectral theory.Cambridge Tracts in Mathematics, 92. Cambridge University Press, Cambridge, 1990. x+197 pp. ISBN: 0-521-40997-7 MR1103113 (92a:35035)
  8. Deya, A. and Gubinelli, M. and Tindel, S. (2011). Non-linear Rough Heat Equations. To appear in Probab. Theory Related Fields.
  9. Diehl, J. and Friz, P. (2011). Backward stochastic differential equations with rough drivers. To appear in Ann. Probab.
  10. Friz, Peter; Oberhauser, Harald. A generalized Fernique theorem and applications. Proc. Amer. Math. Soc. 138 (2010), no. 10, 3679--3688. MR2661566 (2011i:60065)
  11. Friz, Peter; Victoir, Nicolas. Euler estimates for rough differential equations. J. Differential Equations 244 (2008), no. 2, 388--412. MR2376201 (2009j:60151)
  12. bibitem Friz, P. and Victoir, N. (2010). {it Multidimensional dimensional processes seen as rough paths}. Cambridge University Press. MR{2604669}
  13. Gubinelli, M. Controlling rough paths. J. Funct. Anal. 216 (2004), no. 1, 86--140. MR2091358 (2005k:60169)
  14. Gubinelli, M. and Lejay, A. and Tindel, S. (2006). Young integrals and SPDEs. Potential Anal., 25, 307-326.
  15. Gubinelli, Massimiliano; Tindel, Samy. Rough evolution equations. Ann. Probab. 38 (2010), no. 1, 1--75. MR2599193 (2011b:60261)
  16. Jentzen, A. and Roeckner, M. (2010). Regularity Analysis for Stochastic Partial Differential Equations with Nonlinear Multiplicative Trace Class Noise. ArXiv preprint.
  17. Lyons, Terry J. Differential equations driven by rough signals. Rev. Mat. Iberoamericana 14 (1998), no. 2, 215--310. MR1654527 (2000c:60089)
  18. Lyons, Terry; Qian, Zhongmin. System control and rough paths.Oxford Mathematical Monographs. Oxford Science Publications.Oxford University Press, Oxford, 2002. x+216 pp. ISBN: 0-19-850648-1 MR2036784 (2005f:93001)
  19. Pazy, A. Semigroups of linear operators and applications to partial differential equations.Applied Mathematical Sciences, 44. Springer-Verlag, New York, 1983. viii+279 pp. ISBN: 0-387-90845-5 MR0710486 (85g:47061)
  20. Prüss, Jan; Sohr, Hermann. Imaginary powers of elliptic second order differential operators in $Lsp p$-spaces. Hiroshima Math. J. 23 (1993), no. 1, 161--192. MR1211773 (94d:47051)
  21. Runst, Thomas; Sickel, Winfried. Sobolev spaces of fractional order, Nemytskij operators, and nonlinear partial differential equations.de Gruyter Series in Nonlinear Analysis and Applications, 3. Walter de Gruyter & Co., Berlin, 1996. x+547 pp. ISBN: 3-11-015113-8 MR1419319 (98a:47071)
  22. Seeley, R. Interpolation in $Lsp{p}$ with boundary conditions.Collection of articles honoring the completion by Antoni Zygmund of 50 years of scientific activity, I. Studia Math. 44 (1972), 47--60. MR0315432 (47 #3981)
  23. Sickel, Winfried. Composition operators acting on Sobolev spaces of fractional order—a survey on sufficient and necessary conditions. Function spaces, differential operators and nonlinear analysis (Paseky nad Jizerou, 1995), 159--182, Prometheus, Prague, 1996. MR1480936 (98j:47158)
Bookmark and Share


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.