Precise asymptotics for infinite dimensional Ito-Lyons maps of Brownian rough paths
Seminar Room 2, Newton Institute Gatehouse
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).