Brown运动的拟必然极性函数

QUASI SURE POLAR FUNCTIONS FOR BROWNIAN MOTION

本文利用Malliavin分析,刻划了d维Brown运动ω(t)的一类拟必然极性函数,即设f(·):R^+→R^d,则在一定条件下,C_{ t>0使ω(t)=f(t)}=0,同时还给出了容度大偏差lim 1/x^2 logC_{‖ω‖_T>x}=-1/2T的二一简单证明。

In terms of Malliavin calculus, We characterize some kind of quasi sure polar functions for d dimensional Brownian motion ω(t), that is, under certain condition for f(·): R^+→R^d, d>2+тр implies C_(т,р){ t>0 s.t. ω(t)=f(t)}=0. We also give a simple proof of the large deviation principle lim(x→0)^(1/x^2)logC_(т,р){‖ω‖_т>x}=—1/2T.