中文摘要：

本文利用大偏差小偏差研究得到布朗运动的一个局部泛函极限定理，证明了在拟必然收敛意义下布朗运动增量关于（r，p）一容度局部泛函极限的收敛速度．

英文摘要：

In this paper the local functional limit theorem for increments of a Brownian motion is derived with large and small deviations, and the local functional convergence rate for increments of Brownian motion in HSlder norm with respect to （r, p）-capacity is estimated.