H¨older 范数下关于Brown 运动增量的泛函局部收敛速度

摘要

本文研究了Brown运动在H¨older范数与容度下的泛函极限问题。利用大偏差小偏差方法，获得了Brown运动增量局部泛函极限的收敛速度，推广了文[4]中的结果。%In this paper, the local functional limit theorem for increments of a Brownian motion is derived. With large and small deviations, the local functional convergence rate for increments of Brownian motion in H¨older norm with respect to capacity is estimated, and the result in [4] is generalized.