独立情形下自正则和的精确渐近性Precise asymptotics for self-normalized sums of independent and identically distributed random variables
付宗魁;吴群英;
摘要(Abstract):
研究均值为零非退化的独立同分布的随机变量序列正则和收敛性,在适当条件下,获得了自正则和精确渐近性的一般结果.
关键词(KeyWords): 独立同分布;自正则和;精确渐近性
基金项目(Foundation): 国家自然科学基金(11361019);; 广西自然科学基金(2013GXNSFDA019001);; 广西高校人才小高地建设创新团队资助计划(桂教人[2011]47号)
作者(Authors): 付宗魁;吴群英;
参考文献(References):
- [1]Hall P,Heyde C C.Martingale Limit Theory and Its Applications[M].New York:Academic Press,1980.
- [2]孙晓祥,杨丽娟.独立情形下一阶矩收敛的精确渐近性的注记[J].吉林大学学报,2013,51(5):871-875.
- [3]Zhao Y X.Asymptotic properties of the moment convergence for NA sequences[J].Acta Mathematica Scientia,2014,34B(2):301-312.
- [4]Zhao Y X,Tao J X.Precise asymptotics in complete moment convergence for self-normalized sums[J].Computers and Mathematics with Applications,2008,56:1779-1786.
- [5]Zang Q P.A kind of complete moment convergence for self-normalized sums[J].Computers and Mathematics with Applications,2010,60:1803-1809.
- [6]Gine E,Gotze F,Masson D M.When is the student t-statistic asymptotically standard normal[J].Ann.Probab,1997,25:1514-1531.
- [7]陆振刚,姜玉秋.自正则部分和精确渐近性的一般结果[J].华东师范大学学报,2013(2):146-153.
- [8]Griffin P S,Kuelbs J.Some extensions of the LIL via self-normalized sums[J].Ann.Probab.,1991,19:380-395.
- [9]Zhang Y,Yang X Y,Dong Z S.A general law of precise asymptotics for the complete moment convergence[J].Chin.Ann.Math.,2009,30B(1):77-90.
- [10]Zang Q P.A general law of complate moment convergence for self-normalized sums[J].Inequalities and Applications,2010,46(1):155-161.