Invariance principles for the law of the iterated logarithm under G-framework  

作　　者：WU PanYu CHEN ZengJing 

机构地区：[1]Qilu Securities Institute for Financial Studies, Shandong University [2]School of Mathematics, Shandong University

出　　处：《Science China Mathematics》2015年第6期1251-1264,共14页中国科学：数学（英文版）

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);National Natural Science Foundation of China(Grant Nos.11471190,11401414 and 11231005);the Natural Science Foundation of Jiangsu Province of China(Grant No.BK20140299)

摘　　要：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.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.

关 键 词：iterated logarithm invariance expectation Brownian continuity union satisfy automatically details 

分 类 号：O211.4[理学—概率论与数理统计]