鞅差序列加权和的几乎处处收敛(英文)
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摘要
本文研究了一类鞅差序列加权和的收敛性的问题.利用一些基本不等式和截尾技术,获得了加权和的几乎处处收敛性,推广了关于独立同分布的随机变量序列的相关结果.
In this paper,we discuss a class of weighted sums for martingale difference sequence based on some elementary inequalities and the truncation technique.The almost sure convergence is obtained,which extends the result on the case of independent identically distributed random variables.
In this paper,we discuss a class of weighted sums for martingale difference sequence based on some elementary inequalities and the truncation technique.The almost sure convergence is obtained,which extends the result on the case of independent identically distributed random variables.
引文
[1]Choi B D,Sung S H.Almost sure convergence theorems of weighted sums of random variables[J].Stoch.Anal.Appl.,1987,5(4):365-377.
[2]Chow Y S.Some convergence theorems for independent random variables[J].Ann.Math.Statist.,1966,37(6):1482-1493.
[3]Chow Y S,Lai T L.Limiting behavior of weighted sums of independent random variables[J].Ann.Probab.,1973,1(5):810-824.
[4]Deng Aijiao,Liu Jingjun.Almost sure convergence and complete convergence for the weighted sums of martingale differences[J].Wuhan Univ.J.Nat.Sci.,1999,4(2):278-284.
[5]Joag-Dev K,Proschan F.Negative association of random variables,with applications[J].Ann.Statist.,1983,11(1):286-295.
[6]Li Guoliang.Bernstein inequality of the sequence of martingale differences and its applications[J].J.of Math.(PRC).,2006,26(1):103-108.
[7]Li Deli,Bhaskara Rao M,Jiang Tiefeng,Wang Xiangchen.Complete convergence and almost sure convergence of weighted sums of random variables[J].J.Theor.Probab.,1995,8(1):49-76.
[8]Stout W F.Some results on the complete and almost sure convergence of linear combinations of independent random variables and martingale differences[J].Ann.Math.Statist.,1968,39(5):1549-1562.
[9]Sung S H.Almost sure conbergence for weighted sums of i.i.d.random variables(II)[J].Bull.Korean Math.Soc,1996,33(3):419-425.
[10]Sung S H.Almost sure conbergence for weighted sums of i.i.d.random variables[J].J.Korean Math.Soc,1997,34(1):57-67.
[11]Teicher H.Almost certain convergence in double arrays[J].Probab.Theory Rel.,1985,69(3):331-345.
[12]Thrum R.A remark on almost sure convergence of weighted sums[J].Probab.Theory Rel.,1987,75(3):425-430.
[13]Tien N D,Hung N V.On the convergence of weighted sums of martingale differences[J].Lect.Notes.Math.,1989,1391:293-307.
[14]Yin Xiaohong,Miao Yu,Yang Qinglong.The estimate of regression function in nonparametric regression model based on exponential martingale difference[J].J.of Math.(PRC).,2007,27(3):279-284.
[2]Chow Y S.Some convergence theorems for independent random variables[J].Ann.Math.Statist.,1966,37(6):1482-1493.
[3]Chow Y S,Lai T L.Limiting behavior of weighted sums of independent random variables[J].Ann.Probab.,1973,1(5):810-824.
[4]Deng Aijiao,Liu Jingjun.Almost sure convergence and complete convergence for the weighted sums of martingale differences[J].Wuhan Univ.J.Nat.Sci.,1999,4(2):278-284.
[5]Joag-Dev K,Proschan F.Negative association of random variables,with applications[J].Ann.Statist.,1983,11(1):286-295.
[6]Li Guoliang.Bernstein inequality of the sequence of martingale differences and its applications[J].J.of Math.(PRC).,2006,26(1):103-108.
[7]Li Deli,Bhaskara Rao M,Jiang Tiefeng,Wang Xiangchen.Complete convergence and almost sure convergence of weighted sums of random variables[J].J.Theor.Probab.,1995,8(1):49-76.
[8]Stout W F.Some results on the complete and almost sure convergence of linear combinations of independent random variables and martingale differences[J].Ann.Math.Statist.,1968,39(5):1549-1562.
[9]Sung S H.Almost sure conbergence for weighted sums of i.i.d.random variables(II)[J].Bull.Korean Math.Soc,1996,33(3):419-425.
[10]Sung S H.Almost sure conbergence for weighted sums of i.i.d.random variables[J].J.Korean Math.Soc,1997,34(1):57-67.
[11]Teicher H.Almost certain convergence in double arrays[J].Probab.Theory Rel.,1985,69(3):331-345.
[12]Thrum R.A remark on almost sure convergence of weighted sums[J].Probab.Theory Rel.,1987,75(3):425-430.
[13]Tien N D,Hung N V.On the convergence of weighted sums of martingale differences[J].Lect.Notes.Math.,1989,1391:293-307.
[14]Yin Xiaohong,Miao Yu,Yang Qinglong.The estimate of regression function in nonparametric regression model based on exponential martingale difference[J].J.of Math.(PRC).,2007,27(3):279-284.