### Precise asymptotics for infinite dimensional Ito-Lyons maps of Brownian rough paths

Kawabi, H *(Okayama)*

Tuesday 06 April 2010, 14:00-15:00

Seminar Room 2, Newton Institute Gatehouse

#### Abstract

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).

#### Presentation