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
We investigate three kinds of strong laws of large numbers for capacities with a new notion of independently and identically distributed(IID) random variables for sub-linear expectations initiated by Peng.It turns out...We investigate three kinds of strong laws of large numbers for capacities with a new notion of independently and identically distributed(IID) random variables for sub-linear expectations initiated by Peng.It turns out that these theorems are natural and fairly neat extensions of the classical Kolmogorov's strong law of large numbers to the case where probability measures are no longer additive. An important feature of these strong laws of large numbers is to provide a frequentist perspective on capacities.展开更多
We obtain a general invariance principle of G-Brownian motion for the law of the iterated logarithm(LIL for short). For continuous bounded independent and identically distributed random variables in G-expectation spac...We obtain a general invariance principle of G-Brownian motion for the law of the iterated logarithm(LIL for short). For continuous bounded independent and identically distributed random variables in G-expectation space, we also give an invariance principle for LIL. In some sense, this result is an extension of the classical Strassen's invariance principle to the case where probability measure is no longer additive. Furthermore,we give some examples as applications.展开更多
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).
基金supported by National Natural Science Foundation of China(Grant No.11231005)
文摘We investigate three kinds of strong laws of large numbers for capacities with a new notion of independently and identically distributed(IID) random variables for sub-linear expectations initiated by Peng.It turns out that these theorems are natural and fairly neat extensions of the classical Kolmogorov's strong law of large numbers to the case where probability measures are no longer additive. An important feature of these strong laws of large numbers is to provide a frequentist perspective on capacities.
基金supported by China Postdoctoral Science Foundation(Grant No.2013M541899)the Natural Science Foundation of Shandong Province of China(Grant Nos.ZR2013AQ021 and ZR2014AM002)+1 种基金National Natural Science Foundation of China(Grant Nos.11471190,11401414 and 11231005)the Natural Science Foundation of Jiangsu Province of China(Grant No.BK20140299)
文摘We obtain a general invariance principle of G-Brownian motion for the law of the iterated logarithm(LIL for short). For continuous bounded independent and identically distributed random variables in G-expectation space, we also give an invariance principle for LIL. In some sense, this result is an extension of the classical Strassen's invariance principle to the case where probability measure is no longer additive. Furthermore,we give some examples as applications.
