Local Functional Limit Theorems of Increments for Brownian Motion  

作　　者：Fu Qing GAO Yong Hong LIU 

机构地区：[1]School of Mathematics and Statistics, Wuhan University, Wuhan 430072, P. R. China [2]Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541004, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2018年第7期1074-1086,共13页数学学报（英文版）

基　　金：Supported by NSFC(Grant Nos.11571262 and 11661025);Science Research Foundation of Guangxi Education Department(Grant No.YB2014117)

摘　　要：In this paper, we present a local Csorgo- Revesz type functional limit theorem for increments of Brownian motion and give its convergence rate. The results also extend the functional forms of Levy＇s modulus of continuity for Brownian motion.In this paper, we present a local Csorgo- Revesz type functional limit theorem for increments of Brownian motion and give its convergence rate. The results also extend the functional forms of Levy＇s modulus of continuity for Brownian motion.

关 键 词：Keywords Brownian motion INCREMENT local functional limit rate of convergence large deviation small deviation 

分 类 号：O211[理学—概率论与数理统计]