非平稳鞅差序列生成的滑动平均过程精确渐近性的一般结果
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摘要
利用非平稳鞅差序列的弱收敛定理和矩不等式,得到了对于相当广泛的边界函数和拟权函数滑动平均过程部分和矩完全收敛性的精确渐近性的一般形式.
By using the weak convergence theorem and the moment inequality of nonstationary martingale difference sequence,we obtained a general form of precise asymptotics in complete moment convergence for sums of moving-average process for more general boundary function and quasi weight function.
By using the weak convergence theorem and the moment inequality of nonstationary martingale difference sequence,we obtained a general form of precise asymptotics in complete moment convergence for sums of moving-average process for more general boundary function and quasi weight function.
引文
[1]Gut A,Sptaru A.Precise Asymptotics in the Baum-Katz and Davis Law of Large Numbers[J].J Math Anal Appl,2000,248(1):233-246.
[2]SU Zhonggen.Precise Asymptotics for Random Matrices and Random Growth Models[J].Acta Math Sinica(Engl Ser),2008,24(6):971-982.
[3]LIU Weidong,LIN Zhenyan.Precise Asymptotics for a New Kind of Complete Moment Convergence[J].Statist Probab Lett,2006,76(16):1787-1799.
[4]FU Ke’ang,ZHANG Lixin.Precise Rates in the Law of the Logarithm for Negatively Associated Random Variables[J].Comput Math Appl,2007,54(5):687-698.
[5]ZHANG Yong,YANG Xiaoyun,DONG Zhishan.A General Law of Precise Asymptotics for the Complete Moment Convergence[J].Chin Ann Math Ser B,2009,30(1):77-90.
[6]TAN Xili,YANG Xiaoyun.The Precise Asymptotics of the Complete Convergence for Moving Average Processes of m-Dependent B-Valued Elements[J].Acta Math Sinica(Engl Ser),2009,25(3):467-480.
[7]ZANG Qingpei,FU Ke’ang.Precise Asymptotics for the Moment Convergence of Moving-Average Process under Dependence[J].Bull Korean Math Soc,2010,47(3):585-592.
[8]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(理学版),2013,51(5):871-875.(SUN Xiaoxiang,YANG Lijuan.A Note on the Precise Asymptotics for the First Moment Convergence of i.i.d.Random Variables[J].Journal of Jilin University(Science Edition),2013,51(5):871-875.)
[9]XING Guodong,YANG Shanchao.On the Precise Rates in the Law of the Logarithm for Positively Associated Sequence[J].RACSAM,2013,107(2):283-297.
[10]XIAO Xiaoyong,YIN Hongwei.Precise Rates in the Law of the Iterated Logarithm for the First Moment Convergence[J].Mediterr J Math,2014,11(1):173-192.
[11]邹广玉.ρ-混合序列部分和之和乘积精确渐近性的一般形式[J].吉林大学学报(理学版),2014,52(4):720-724.(ZOU Guangyu.General Results on Precise Asymptotics for Products of Sums of Partial Sums ofρ-Mixing Sequence[J].Journal of Jilin University(Science Edition),2014,52(4):720-724.)
[12]JIANG Hui,YU Lei.Precise Asymptotics in Complete Moment Convergence of Parameter Estimator in the Gaussian Autoregressive Process[J].Comm Statist Theory Methods,2015,44(7):1483-1496.
[13]曾艳,王文胜.鞅差序列生成的线性过程的Baum-Katz大数定律的精确渐近性[J].杭州师范大学学报(自然科学版),2009,8(6):414-418.(ZENG Yan,WANG Wensheng.Precise Asymptotics in the Baum-Katz Law of Large Numbers for Linear Processes of Martingale Difference Sequences[J].Journal of Hangzhou Normal University(Natural Science Edition),2009,8(6):414-418.)
[14]曾艳,王文胜.鞅差序列生成的线性过程的精确渐近性[J].高师理科学刊,2010,30(4):1-4.(ZENG Yan,WANG Wensheng.Precise Asymptotics for Linear Processes of Martingale Difference Sequences[J].Journal of Science of Teachers’College and University,2010,30(4):1-4.)
[15]韩玉,杨晓云,董志山.由鞅差所产生的非平稳线性过程的随机泛函中心极限定理[J].吉林大学学报(理学版),2005,43(6):716-724.(HAN Yu,YANG Xiaoyun,DONG Zhishan.A Functional Central Limit Theorem for the Random Sum of Linear Process of Martingale Differences[J].Journal of Jilin University(Science Edition),2005,43(6):716-724.)
[16]Hall P,Heyde C C.Martingale Limit Theory and Its Application[M].New York:Academic Press,1980.
[2]SU Zhonggen.Precise Asymptotics for Random Matrices and Random Growth Models[J].Acta Math Sinica(Engl Ser),2008,24(6):971-982.
[3]LIU Weidong,LIN Zhenyan.Precise Asymptotics for a New Kind of Complete Moment Convergence[J].Statist Probab Lett,2006,76(16):1787-1799.
[4]FU Ke’ang,ZHANG Lixin.Precise Rates in the Law of the Logarithm for Negatively Associated Random Variables[J].Comput Math Appl,2007,54(5):687-698.
[5]ZHANG Yong,YANG Xiaoyun,DONG Zhishan.A General Law of Precise Asymptotics for the Complete Moment Convergence[J].Chin Ann Math Ser B,2009,30(1):77-90.
[6]TAN Xili,YANG Xiaoyun.The Precise Asymptotics of the Complete Convergence for Moving Average Processes of m-Dependent B-Valued Elements[J].Acta Math Sinica(Engl Ser),2009,25(3):467-480.
[7]ZANG Qingpei,FU Ke’ang.Precise Asymptotics for the Moment Convergence of Moving-Average Process under Dependence[J].Bull Korean Math Soc,2010,47(3):585-592.
[8]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(理学版),2013,51(5):871-875.(SUN Xiaoxiang,YANG Lijuan.A Note on the Precise Asymptotics for the First Moment Convergence of i.i.d.Random Variables[J].Journal of Jilin University(Science Edition),2013,51(5):871-875.)
[9]XING Guodong,YANG Shanchao.On the Precise Rates in the Law of the Logarithm for Positively Associated Sequence[J].RACSAM,2013,107(2):283-297.
[10]XIAO Xiaoyong,YIN Hongwei.Precise Rates in the Law of the Iterated Logarithm for the First Moment Convergence[J].Mediterr J Math,2014,11(1):173-192.
[11]邹广玉.ρ-混合序列部分和之和乘积精确渐近性的一般形式[J].吉林大学学报(理学版),2014,52(4):720-724.(ZOU Guangyu.General Results on Precise Asymptotics for Products of Sums of Partial Sums ofρ-Mixing Sequence[J].Journal of Jilin University(Science Edition),2014,52(4):720-724.)
[12]JIANG Hui,YU Lei.Precise Asymptotics in Complete Moment Convergence of Parameter Estimator in the Gaussian Autoregressive Process[J].Comm Statist Theory Methods,2015,44(7):1483-1496.
[13]曾艳,王文胜.鞅差序列生成的线性过程的Baum-Katz大数定律的精确渐近性[J].杭州师范大学学报(自然科学版),2009,8(6):414-418.(ZENG Yan,WANG Wensheng.Precise Asymptotics in the Baum-Katz Law of Large Numbers for Linear Processes of Martingale Difference Sequences[J].Journal of Hangzhou Normal University(Natural Science Edition),2009,8(6):414-418.)
[14]曾艳,王文胜.鞅差序列生成的线性过程的精确渐近性[J].高师理科学刊,2010,30(4):1-4.(ZENG Yan,WANG Wensheng.Precise Asymptotics for Linear Processes of Martingale Difference Sequences[J].Journal of Science of Teachers’College and University,2010,30(4):1-4.)
[15]韩玉,杨晓云,董志山.由鞅差所产生的非平稳线性过程的随机泛函中心极限定理[J].吉林大学学报(理学版),2005,43(6):716-724.(HAN Yu,YANG Xiaoyun,DONG Zhishan.A Functional Central Limit Theorem for the Random Sum of Linear Process of Martingale Differences[J].Journal of Jilin University(Science Edition),2005,43(6):716-724.)
[16]Hall P,Heyde C C.Martingale Limit Theory and Its Application[M].New York:Academic Press,1980.