Etimology: Ecru describes the shade greyish-pale yellow or a light greyish-yellowish brown. It is often used to describe such fabrics as silk and linen in their unbleached state. Ecru comes from the French word écru, which means literally 'raw' or 'unbleached'.
Coordinates RGB(194, 178, 128). (Wikipedia)

Project

This project gathers a group of French researchers who have been and are interested in using rough path theory to address problem from stochastic analysis but also find new and useful ways to take the idea of a rough path to other, less conventional, contexts.

Main vocations of the project

• consolidate collaborations between the participants;
• build bridges to related and nearby fields of mathematics and physics (numerical mathematics, algebra, classical partial differential equations, quantum field theory and renormalization) via invitation to experts from these fields to give us tutorials and to collaborate with us ;
• propose a lively and competitive environment for students and post-docs who would like to understand the theory and get involved in the current research;
• contribute to popularize rough path ideas in the mathematical community via lecture notes, workshops, etc...

People

• Laure Coutin (Laboratoire de Statistique et Probabilités, Université Toulouse III) (home)
• Massimiliano Gubinelli (CEREMADE, Paris Dauphine) (home)
• Antoine Lejay (IECN, INRIA) (home)
• Ivan Nourdin (LPMA, Paris 6) (home)
• Samy Tindel (IECN, Nancy 1) (home)
• Jeremie Unterberger (IECN, Nancy 1) (home)
• Lorenzo Zambotti (LPMA, Paris 6) (home)

Events

• Workshop "Rough paths in interaction", 10-11 June 2010, Institut Henri Poincaré, Paris. (page)

Rough paths

The theory of rough paths allows to define integrals of differential forms against irregular paths and differential equations controlled by irregular paths. This theory makes use of an extension of the notion of iterated integrals of the paths, whose algebraic properties appear to be fundamental. Stochastic processes give natural class of paths for which such integrals or differential equations are required, and this theory may be used for many types of stochastic processes.

Terry Lyons introduced the notion of rough paths in 1998 in the paper Differential equations driven by rough signals (PDF), later developed in the book "System Control and Rough Paths" (link) by T. Lyons and Z. Qian.

Other more recent references on the basic theory:

• Lyons' St. Flour notes: Differential Equations Driven by Rough Paths, Ecole d'Eté de Probabilité de Saint-Flour XXXIV-2004 by Terry J. Lyons, Michael J. Caruana, Thierry Lévy, Lecture Notes in Mathematics, Springer, ISSN 0721-5363.
• Yet another introduction to rough paths by Antoine Lejay. In: Séminaire de probabilités XLII, Lecture Notes in Mathematics 1979, Springer-Verlag, 1-101 (2009) (hal) (journal).
• P. Friz and N. Victoir. Multidimensional Stochastic Processes as Rough Paths. Theory and Applications. Cambridge Studies of Advanced Mathematics, Cambridge University Press, 2010 (amazon)

Bibliography