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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


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).


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