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Inequalities of Maximum of Partial Sums and Weak Convergence for a Class of Weak Dependent Random Variables

✍ Scribed by Jiang Feng Wang; Feng Bin Lu

Publisher
Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
Year
2005
Tongue
English
Weight
169 KB
Volume
22
Category
Article
ISSN
1439-7617

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πŸ“œ SIMILAR VOLUMES

Some Inequalities for the Maximum of Par
Some Inequalities for the Maximum of Partial Sums of Random Variables
✍ J. MogyorΓ³di πŸ“‚ Article πŸ“… 1975 πŸ› John Wiley and Sons 🌐 English βš– 623 KB

is non-decreasing. Thus, if one applies the c,-inequality, the inequality follows trivially. From this and from the preceding inequality we obtain By our condition the sums on the right hand side converge to 0 as n -+ + 00. This proves the assertion. Remarks. It is easy to see that for p > 2 our c

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✍ G. Siegel πŸ“‚ Article πŸ“… 1978 πŸ› John Wiley and Sons 🌐 English βš– 526 KB

Let mlzk be a median of X,, and put S, = X,, + + X , + . . . +Xnkrt-A,, where {A,, n= 1, 2, . . .} is a sequence of constants. S, and X,, are subject to F, and F,,, respectively. The problem is the existence of a non-defective limit distribution for {Fn, n = 1, 2, . . .} in the sence of weak conver