scholarly journals LIMITING BEHAVIOR OF THE MAXIMUM OF THE PARTIAL SUM FOR NEGATIVELY SUPERADDITIVE DEPENDENT RANDOM VARIABLES

2015 ◽  
Vol 28 (3) ◽  
pp. 409-417
Author(s):  
HYUN-CHULL KIM
Keyword(s):  
Random Variables ◽  
Dependent Random Variables ◽  
Limiting Behavior ◽  
Partial Sum

scholarly journals Limiting Behavior of the Maximum of the Partial Sum for Linearly Negative Quadrant Dependent Random Variables under Residual Cesàro Alpha-Integrability Assumption

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Jiangfeng Wang ◽  
Qunying Wu
Keyword(s):  
Complete Convergence ◽  
Random Variables ◽  
Dependence Structure ◽  
Dependent Random Variables ◽  
Limiting Behavior ◽  
Partial Sum ◽  
Convergence Results ◽  
Negative Quadrant Dependence ◽  
Quadrant Dependence

Linearly negative quadrant dependence is a special dependence structure. By relating such conditions to residual Cesàro alpha-integrability assumption, as well as to strongly residual Cesàro alpha-integrability assumption, someLp-convergence and complete convergence results of the maximum of the partial sum are derived, respectively.

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.

On the asymptotic independent representations for sums of some weakly dependent random variables

2006 ◽  
Vol 43 (1) ◽  
pp. 33-46
Author(s):  
Rafik Aguech ◽  
Sana Louhichi ◽  
Sofyen Louhichi
Keyword(s):  
Positive Integer ◽  
Random Variables ◽  
Triangular Array ◽  
Independent Random Variables ◽  
Dependent Random Variables ◽  
Limiting Behavior ◽  
Weakly Dependent Random Variables ◽  
Weakly Dependent

Let, for each n?N, (Xi,n)0?i?nbe a triangular array of stationary, centered, square integrable and associated real valued random variables satisfying the weakly dependence condition lim N?N0limsup n?+8nSr=NnCov (X0,n, Xr,n)=0;where N0is either infinite or the first positive integer Nfor which the limit of the sum nSr=NnCov (X0,n, Xr,n) vanishes as n goes to infinity. The purpose of this paper is to build, from (Xi,n)0?i?n, a sequence of independent random variables (X˜i,n)0?i?nsuch that the two sumsSi=1nXi,nandSi=1nX˜i,nhave the same asymptotic limiting behavior (in distribution).

Asymptotics for the partial sum and its maximum of dependent random variables*

2017 ◽  
Vol 57 (1) ◽  
pp. 142-153 ◽  
Author(s):  
Ting Zhang ◽  
Xi-Nian Fang ◽  
Jie Liu ◽  
Yang Yang
Keyword(s):  
Random Variables ◽  
Dependent Random Variables ◽  
Partial Sum

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

1976 ◽  
Vol 13 (02) ◽  
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, S 1, …, Sn ) where Sk is the kth partial sum of a finite sequence of exchangeable random variables X 1, …, 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.

Limiting behavior of generalized delayed average of random sequence

2014 ◽  
Vol 64 (4) ◽  
Author(s):  
Zhong-zhi Wang ◽  
Wen-bo Chen
Keyword(s):  
Likelihood Ratio ◽  
Laplace Transformation ◽  
Random Sequence ◽  
Random Variables ◽  
Dependent Random Variables ◽  
Limiting Behavior ◽  
Delayed Sums ◽  
Log Likelihood ◽  
Log Likelihood Ratio

AbstractLet (ξ n)n∈N be a sequence of arbitrarily dependent random variables, and let $$T_{a_n ,k_n }$$ be delayed sums. By virtue of the notion of asymptotic delayed log-likelihood ratio and Laplace transformation, the almost sure limiting behavior of the generalized delayed averages $$\frac{1} {{k_n }}T_{a_n ,k_n }$$ is investigated, of which the results generalize and improve some work of Liu.

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