关于sup(n≥1)|S_n/n(1/r)|(0〈r〈2)和sup(n≥1)|S_n/■|的矩

On Moments of sup(n≥1)|S_n/n(1/r)|(0<r<2) andsup(n≥1)|S_n/■|

设 {Xn,n≥ 1 }是 φ-混合的同分布的随机变量序列 ,记 Sn=∑ni=1Xi( n≥ 1 ) .该文的目的是要在一定的矩条件和混合速度限制下 ,讨论了 supn≥ 1| Snn1/ r| ( 0 <r <2 )和 supn≥ 1| Snnlnlnn|

Let {X\-n,n≥1} be a φ mixing sequence of identically distributed random variables, and S\-n=∑ni=1X\-i(n≥1). In the paper, the authors will study the moments of sup n≥1S\-nn\+\{1/r\}(0<r<2) and sup n≥1S\-nn lnln n under the conditions of some moments and the rate of mixing.