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

  • Bally, V. and Caramellino, L.: Regularity of probability laws by using an interpolation method. arXiv:1211.0052v1, Preprint, (2012).
  • Champagnat, N. and Jabin, P.,E.: Strong solutions to stochastic differential equations with rough coefficients. arXiv:1303.2611, Preprint, (2014).
  • Cherny, Alexander S.; Engelbert, Hans-Jürgen. Singular stochastic differential equations. Lecture Notes in Mathematics, 1858. Springer-Verlag, Berlin, 2005. viii+128 pp. ISBN: 3-540-24007-1 MR2112227
  • De Marco, Stefano. Smoothness and asymptotic estimates of densities for SDEs with locally smooth coefficients and applications to square root-type diffusions. Ann. Appl. Probab. 21 (2011), no. 4, 1282--1321. MR2857449
  • Debussche, Arnaud; Fournier, Nicolas. Existence of densities for stable-like driven SDE's with Hölder continuous coefficients. J. Funct. Anal. 264 (2013), no. 8, 1757--1778. MR3022725
  • Debussche, Arnaud; Romito, Marco. Existence of densities for the 3D Navier-Stokes equations driven by Gaussian noise. Probab. Theory Related Fields 158 (2014), no. 3-4, 575--596. MR3176359
  • Evans, Lawrence C. Partial differential equations. Graduate Studies in Mathematics, 19. American Mathematical Society, Providence, RI, 1998. xviii+662 pp. ISBN: 0-8218-0772-2 MR1625845
  • Fournier, Nicolas; Printems, Jacques. Absolute continuity for some one-dimensional processes. Bernoulli 16 (2010), no. 2, 343--360. MR2668905
  • Friedman, Avner. Partial differential equations of parabolic type. Prentice-Hall, Inc., Englewood Cliffs, N.J. 1964 xiv+347 pp. MR0181836
  • Grafakos, Loukas. Classical Fourier analysis. Second edition. Graduate Texts in Mathematics, 249. Springer, New York, 2008. xvi+489 pp. ISBN: 978-0-387-09431-1 MR2445437
  • Gyöngy, Istvàn; Martìnez, Teresa. On stochastic differential equations with locally unbounded drift. Czechoslovak Math. J. 51(126) (2001), no. 4, 763--783. MR1864041
  • Hayashi, Masafumi; Kohatsu-Higa, Arturo; Yûki, Gô. Local Hölder continuity property of the densities of solutions of SDEs with singular coefficients. J. Theoret. Probab. 26 (2013), no. 4, 1117--1134. MR3119987
  • Karatzas, Ioannis; Shreve, Steven E. Brownian motion and stochastic calculus. Second edition. Graduate Texts in Mathematics, 113. Springer-Verlag, New York, 1991. xxiv+470 pp. ISBN: 0-387-97655-8 MR1121940
  • Krylov, N. V. Lectures on elliptic and parabolic equations in Hölder spaces. Graduate Studies in Mathematics, 12. American Mathematical Society, Providence, RI, 1996. xii+164 pp. ISBN: 0-8218-0569-X MR1406091
  • Krylov, N. V.; Röckner, M. Strong solutions of stochastic equations with singular time dependent drift. Probab. Theory Related Fields 131 (2005), no. 2, 154--196. MR2117951
  • Kusuoka, Shigeo; Stroock, Daniel. Applications of the Malliavin calculus. I. Stochastic analysis (Katata/Kyoto, 1982), 271--306, North-Holland Math. Library, 32, North-Holland, Amsterdam, 1984. MR0780762
  • Ladyzenskaja, O.,A., Solonnikov, V.,A. and Ural'ceva, N.,N.: Linear and Quasi-linear Equations of Parabolic Type. Transl.,Math.,Monogr., Amer.,Math.,Soc., Providence, (1968). MR0241822
  • Stein, Elias M.; Shakarchi, Rami. Functional analysis. Introduction to further topics in analysis. Princeton Lectures in Analysis, 4. Princeton University Press, Princeton, NJ, 2011. xviii+423 pp. ISBN: 978-0-691-11387-6 MR2827930
  • Nualart, David. The Malliavin calculus and related topics. Second edition. Probability and its Applications (New York). Springer-Verlag, Berlin, 2006. xiv+382 pp. ISBN: 978-3-540-28328-7; 3-540-28328-5 MR2200233
  • Shigekawa, Ichiro. Stochastic analysis. Translated from the 1998 Japanese original by the author. Translations of Mathematical Monographs, 224. Iwanami Series in Modern Mathematics. American Mathematical Society, Providence, RI, 2004. xii+182 pp. ISBN: 0-8218-2626-3 MR2060917
  • Tanaka, A.: The Existence of the Densities of Solutions of Elliptic Type SDEs with Non-smooth Drift Coefficients. Master Thesis of Osaka Univ., (2010 in Japanese).
  • Zhang, Xicheng. Strong solutions of SDES with singular drift and Sobolev diffusion coefficients. Stochastic Process. Appl. 115 (2005), no. 11, 1805--1818. MR2172887
Bookmark and Share


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