Acta mathematica scientia,Series B

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ON THE LIMITING BEHAVIOR OF THE MAXIMUM PARTIAL SUMS FOR ARRAYS OF ROWWISE NA RANDOM VARIABLES

Gan Shixin; Chen Pingyan   

  1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
  • Received:2004-02-10 Revised:1900-01-01 Online:2007-04-20 Published:2007-04-20
  • Contact: Gan Shixin

Abstract:

Let {Xni, 1≤ n,i<∞} be an array of rowwise NA random variables and
{an,n≥1} a sequence of constants with 0n↑∞. The limiting behavior of maximum partial sums $\frac{1}{a_n}\max\limits_{1\leq k\leq n}|\sum\limits^k_{i=1}X_{ni}|$ is investigated and some new results are obtained. The results extend and improve the corresponding theorems of rowwise independent random variable arrays by Hu and Taylor [1] and
Hu and Chang [2].

Key words: NA random variable, maximum partial sum, complete convergence, convergence in probability

CLC Number: 

  • 60F15
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