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 ...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).展开更多
基金The work is supported by NSFC(No.11661025)Science Research Foundation of Guangxi Education department(No.YB2014117)+1 种基金Guangxi Programme for Promoting Young Teachers's Ability(No.2017KY0191)Innovative Programme for University(No.201510595198)
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)+6 种基金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 ProvinceWCU (World Class University) Program of Korea Science and Engineering Foundation (Grant No. R31-20007)
文摘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).