SUMMER SCHOOL
Paraproducts and Analysis of Rough Paths

1-5 Basics
6-9 The signature
10-13 Applications
14-16 Paraproducts and rough paths

  1. Differential equations driven by rough paths: an approach via discrete approximation.
    by A. Davie
    Appl. Math. Res. Express. AMRX 2007, no. 2, Art. ID abm009, 40 pp (2007)

    [presenter: Yujia Zhai]

  2. Controlling rough paths. Part I
    by M. Gubinelli
    J. Funct. Anal. 216 (2004), no. 1, 86-140.

    [presenter: Cristina Benea]

  3. Controlling rough paths. Part II
    by M. Gubinelli
    J. Funct. Anal. 216 (2004), no. 1, 86-140.

    [presenter: Gianmarco Brocchi]

  4. Ramification of rough paths.
    by M. Gubinelli
    J. Differential Equations 248 (2010), no. 4, 693-721.

    [presenter: Robert Crowell]
  5. Integrability and tail estimates for Gaussian rough differential equations.
    by T. Cass, C. Litterer, and T. Lyons
    Ann. Probab. 41 (2013), no. 4, 3026-3050.

    [presenter: Luigi Borasi]

  6. Inverting the signature of a path
    by T. Lyons, W. Xu
    arXiv:1406.7833

    [presenter: Joao Ramos]

  7. Characteristic functions of measures on geometric rough paths.
    by I. Chevyrev and T. Lyons
    arXiv:1307.3580 .

    [presenter: Michal Warchalski]

  8. Decay Rate of Iterated Integrals of Branched Rough Paths
    by H. Boedihardjo
    arXiv:1501.05641 .

    [presenter: Marco Fraccaroli ]

  9. Physical Brownian motion in magnetic field as rough path
    by P. Friz, P. Gassiat, T. Lyons
    Trans. Amer. Math. Soc. 367 (2015), no. 11, 7939-7955.

    [presenter: Kevin O'Neill]

  10. Reflected rough differential equations.
    by A. Shigeki
    Stochastic Process. Appl. 125 (2015), no. 9, 3570–3595.
    Skip section 5 if time runs out.
    [presenter: Joris Roos]

  11. Rough solutions for the periodic Korteweg–de Vries equation.
    by M. Gubinelli
    Commun. Pure Appl. Anal. 11 (2012), no. 2, 709-733.

    [presenter: Jonas Jansen ]

  12. Deterministic homogenization for fast-slow systems with chaotic noise
    by D. Kelly and I. Melbourne
    arXiv:1409.5748 .

    [presenter: Johanna Richter]

  13. A signed measure on rough paths associated to a PDE of high order: results and conjectures.
    by D. Levin and T. Lyons
    Rev. Mat. Iberoam. 25 (2009), no. 3, 971-994.

    [presenter: Gennady Uraltsev]

  14. The partial sum process of orthogonal expansions as geometric rough process with Fourier series as an example—an improvement of Menshov-Rademacher theorem.
    by T. Lyons and D. Yang
    J. Funct. Anal. 265 (2013), no. 12, 3067-3103.
    Put less emphasis on Fourier series, if time runs out.
    [presenter: Dominique Maldague]

  15. Paracontrolled distributions and singular PDEs.
    by M. Gubinelli, P. Imkeller, N. Perkowski
    Forum Math. Pi 3 (2015), e6, 75 pp.
    Do RDE, skip Burgers and PAM.
    [presenter: Immanual Zachhuber]

  16. The Nash-Moser theorem and paradifferential operators.
    by L. Hörmander
    Analysis, et cetera, 429-449, Academic Press, Boston, MA, 1990.

    [presenter: Polona Durcik]

  17. Geometric versus Non-Geometric Rough Paths.
    by M. Hairer, D. Kelly
    Annales de l'Institut Henri Poincare, Probabilites et Statistiques 51, no. 1 (February 2015): 207{51. doi:10.1214/13-AIHP564 Analysis, et cetera, 429-449, Academic Press, Boston, MA, 1990.
    Do theorem 1.9, skip sections 3 and 5.
    [presenter: Nikolay Barashkov]

  18. Quasilinear SPDE via rough paths.
    by F. Otto, and H. Weber
    Preprint, arXiv:1605.09744 .

    [presenter: Pavel Zorin-Kranich]

  19. The continuous Anderson hamiltonian in dimension two
    by R. Allez and K. Chouk
    Preprint, arXiv:1511.02718 .

    [presenter: Irina Holmes]