How big are the increments of G-Brownian motion?  

作　　者：HU Feng CHEN ZengJing ZHANG DeFei 

机构地区：[1]School of Mathematical Sciences, Qufu Normal University [2]School of Mathematics, Shandong University [3]Department of Financial Engineering, Ajou University [4]Department of Mathematics, Honghe University

出　　处：《Science China Mathematics》2014年第8期1687-1700,共14页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant Nos. 11301295 and 11171179);supported by National Natural Science Foundation of China (Grant Nos. 11231005 and 11171062);supported by National Natural Science Foundation of China (Grant No. 11301160);Natural Science Foundation of Yunnan Province of China (Grant No. 2013FZ116);Doctoral Program Foundation of Ministry of Education of China (Grant Nos. 20123705120005 and 20133705110002);Postdoctoral Science Foundation of China (Grant No. 2012M521301);Natural Science Foundation of Shandong Province of China (Grant Nos. ZR2012AQ009 and ZR2013AQ021);Program for Scientific Research Innovation Team in Colleges and Universities of Shandong Province;WCU (World Class University) Program of Korea Science and Engineering Foundation (Grant No. R31-20007)

摘　　要：In this paper,we investigate the problem:How big are the increments of G-Brownian motion.We obtain the Csrg and R′ev′esz’s type theorem for the increments of G-Brownian motion.As applications of this result,we get the law of iterated logarithm and the Erds and R′enyi law of large numbers for G-Brownian motion.Furthermore,it turns out that our theorems are natural extensions of the classical results obtained by Csrg and R′ev′esz(1979).In this paper,we investigate the problem：How big are the increments of G-Brownian motion.We obtain the Csrg and R′ev′esz’s type theorem for the increments of G-Brownian motion.As applications of this result,we get the law of iterated logarithm and the Erds and R′enyi law of large numbers for G-Brownian motion.Furthermore,it turns out that our theorems are natural extensions of the classical results obtained by Csrg and R′ev′esz（1979）.

关 键 词：sublinear expectation capacity G-normal distribution G-Brownian motion increments of GBrownian motion law of iterated logarithm 

分 类 号：O211.67[理学—概率论与数理统计]