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Workshop Programme

for period 6 - 7 April 2010

Rough Paths, SPDEs and Related Topics

6 - 7 April 2010


Tuesday 6 April
09:00-10:00 Lejay, A (INRIA)
  An introduction to rough paths Sem 2

This talk aims at being a gentle introduction to the theory of rough paths, whose goal is to define integrals along irregular paths, as well as solutions of controlled differential equation controlled by rough paths. In particular, we endow the importance on the continuity with respect to the "smooth case" and show that the equivalent of the "iterated integrals" of the paths we integrate contain all the information needed to construct integrals and solve differential equations driven by irregular paths.

10:00-11:00 Von Renesse, M (Leipzig)
  Ergodicity of stochastic curve shortening flow Sem 2
11:00-12:00 Souganidis, T (Chicago)
  Fully nonlinear second order pde with rough paths and stochastic viscosity solutions Sem 2
12:00-13:00 Hairer, M (Warwick)
  Stochastic Burgers equations and rough paths Sem 2
13:00-14:00 Lunch
14:00-15:00 Kawabi, H (Okayama)
  Precise asymptotics for infinite dimensional Ito-Lyons maps of Brownian rough paths Sem 2

In this talk, we discuss precise asymptotics for the laws of solutions of ''formal'' Stratonovich type SDEs on Banach spaces. We give a rigorous meaning of the solution through RDEs in the rough path theory initiated by T. Lyons. The main example we have in mind is a loop group-valued Brownian motion introduced by P. Malliavin. In our proof of the main theorem (asymptotic expansion formula of the Laplace type functional integral), a generalisation of Ledoux-Qian-Zhang's large deviation result and a ''stochastic'' Taylor expansion in the sense of rough paths play important roles. This talk is based on joint work with Yuzuru Inahama (Nagoya University).

15:00-16:00 Crisan, D (Imperial College)
  An application of the Kusuoka-Lyons-Victoir cubature method to the numerical solution of BSDEs Sem 2
16:00-17:00 Soner, M (ETH Zuerich)
  Financial markets with uncertain volatility Sem 2
Wednesday 7 April
08:30-09:30 Oberhauser, H (Technische Universitat Berlin)
  A (rough) pathwise approach to some SPDEs Sem 2
10:30-11:30 Gyongy, I (Edinburgh)
  On the rate of convergence of nonlinear filters when the observation processes converge Sem 2
11:30-12:30 Mattingly, J (Duke)
  Malliavin calculus for non-adapted SPDEs Sem 2
12:30-14:00 Lunch
14:00-15:00 Lyons, T (Oxford)
  Evolving communities with individual preferences CMS MR2
15:00-16:00 Lions, PL (Universite Paris-Dauphine)
  Not so rough paths CMS MR2
16:00-17:00 Flandoli, F (Universita di Pisa)
  Examples of regularisation by noise CMS MR2

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