Some convergence properties for partial sums of widely orthant dependent random variables and their statistical applications

2018 ◽  
Vol 61 (4) ◽  
pp. 1663-1684
Author(s):  
Mengmei Xi ◽  
Rui Wang ◽  
Zhaoyang Cheng ◽  
Xuejun Wang
Keyword(s):  
Random Variables ◽  
Partial Sums ◽  
Convergence Properties ◽  
Dependent Random Variables ◽  
Widely Orthant Dependent

scholarly journals Further Spitzer’s law for widely orthant dependent random variables

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Pingyan Chen ◽  
Jingjing Luo ◽  
Soo Hak Sung
Keyword(s):  
Random Variables ◽  
Partial Sums ◽  
Dependent Random Variables ◽  
Moment Conditions ◽  
Widely Orthant Dependent

AbstractThe Spitzer’s law is obtained for the maximum partial sums of widely orthant dependent random variables under more optimal moment conditions.

A note on Spitzer's lemma and its application to the maximum of partial sums of dependent random variables

1976 ◽  
Vol 13 (2) ◽  
pp. 361-364 ◽  
Author(s):  
M. E. Solari ◽  
J. E. A. Dunnage
Keyword(s):  
Infinite Sequence ◽  
Random Variables ◽  
Finite Sequence ◽  
Partial Sums ◽  
Dependent Random Variables ◽  
Finite Segment ◽  
Exchangeable Random Variables ◽  
Partial Sum

We give an expression for the expectation of max (0, S1, …, Sn) where Sk is the kth partial sum of a finite sequence of exchangeable random variables X1, …, Xn. When the Xk are also independent, the formula we give has already been obtained by Spitzer; and when the sequence is a finite segment of an infinite sequence of exchangeable random variables, it is a consequence of a theorem of Hewitt.

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