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Timetable (SPDW06)

Rough Paths, SPDEs and Related Topics

Tuesday 6th April 2010 to Wednesday 7th April 2010

Tuesday 6th April 2010
09:00 to 10:00 A Lejay ([INRIA])
An introduction to rough paths
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.
INI 2
10:00 to 11:00 M Von Renesse ([Leipzig])
Ergodicity of stochastic curve shortening flow
INI 2
11:00 to 12:00 T Souganidis ([Chicago])
Fully nonlinear second order pde with rough paths and stochastic viscosity solutions
INI 2
12:00 to 13:00 M Hairer ([Warwick])
Stochastic Burgers equations and rough paths
INI 2
13:00 to 14:00 Lunch INI 2
14:00 to 15:00 H Kawabi ([Okayama])
Precise asymptotics for infinite dimensional Ito-Lyons maps of Brownian rough paths
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).
INI 2
15:00 to 16:00 D Crisan ([Imperial College])
An application of the Kusuoka-Lyons-Victoir cubature method to the numerical solution of BSDEs
INI 2
16:00 to 17:00 M Soner ([ETH Zuerich])
Financial markets with uncertain volatility
INI 2
Wednesday 7th April 2010
08:30 to 09:30 H Oberhauser (Technische Universität Berlin)
A (rough) pathwise approach to some SPDEs
INI 2
10:30 to 11:30 I Gyongy ([Edinburgh])
On the rate of convergence of nonlinear filters when the observation processes converge
INI 2
11:30 to 12:30 J Mattingly ([Duke])
Malliavin calculus for non-adapted SPDEs
INI 2
12:30 to 14:00 Lunch
14:00 to 15:00 T Lyons (University of Oxford)
Evolving communities with individual preferences
15:00 to 16:00 PL Lions (Université Paris-Dauphine)
Not so rough paths
16:00 to 17:00 F Flandoli (Università di Pisa)
Examples of regularisation by noise
University of Cambridge Research Councils UK
    Clay Mathematics Institute The Leverhulme Trust London Mathematical Society Microsoft Research NM Rothschild and Sons