scholarly journals Weak Convergence Results for Extremal Processes Generated by Dependent Random Variables

1978 ◽  
Vol 6 (4) ◽  
pp. 660-667 ◽  
Author(s):  
Robert J. Adler
Keyword(s):  
Weak Convergence ◽  
Random Variables ◽  
Dependent Random Variables ◽  
Convergence Results ◽  
Extremal Processes

Weak convergence of the adjusted range of cumulative sums of exchangeable random variables

1983 ◽  
Vol 20 (02) ◽  
pp. 297-304 ◽  
Author(s):  
Brent M. Troutman
Keyword(s):  
Weak Convergence ◽  
Asymptotic Distribution ◽  
Random Variables ◽  
Dependent Random Variables ◽  
Random Functions ◽  
Exchangeable Random Variables ◽  
Convergence Results ◽  
Cumulative Sums

Let be the adjusted range of the cumulative sums of a sequence , where . Weak convergence results for random functions constructed from cumulative sums of {Xs } are used to obtain the asymptotic distribution and moments of when {Xs } are exchangeable, or symmetrically dependent, random variables.

Weak convergence of the adjusted range of cumulative sums of exchangeable random variables

1983 ◽  
Vol 20 (2) ◽  
pp. 297-304 ◽  
Author(s):  
Brent M. Troutman
Keyword(s):  
Weak Convergence ◽  
Asymptotic Distribution ◽  
Random Variables ◽  
Dependent Random Variables ◽  
Random Functions ◽  
Exchangeable Random Variables ◽  
Convergence Results ◽  
Cumulative Sums

Let be the adjusted range of the cumulative sums of a sequence , where . Weak convergence results for random functions constructed from cumulative sums of {Xs} are used to obtain the asymptotic distribution and moments of when {Xs} are exchangeable, or symmetrically dependent, random variables.

scholarly journals Complete convergence for weighted sums of widely orthant-dependent random variables

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Pingyan Chen ◽  
Soo Hak Sung
Keyword(s):  
Complete Convergence ◽  
Law Of Large Numbers ◽  
Random Variables ◽  
Weighted Sums ◽  
Dependent Random Variables ◽  
Strong Law ◽  
Link Type ◽  
Convergence Results ◽  
Large Numbers ◽  
Widely Orthant Dependent

AbstractThe complete convergence results for weighted sums of widely orthant-dependent random variables are obtained. A strong law of large numbers for weighted sums of widely orthant-dependent random variables is also obtained. Our results extend and generalize some results of Chen and Sung (J. Inequal. Appl. 2018:121, 2018), Zhang et al. (J. Math. Inequal. 12:1063–1074, 2018), Chen and Sung (Stat. Probab. Lett. 154:108544, 2019), Lang et al. (Rev. Mat. Complut., 2020, 10.1007/s13163-020-00369-5), and Liang (Stat. Probab. Lett. 48:317–325, 2000).

scholarly journals On the necessary condition for Baum-Katz type theorem for non-identically distributed and negatively dependent random fields

2018 ◽  
Vol 72 (2) ◽  
pp. 1
Author(s):  
Zbigniew Łagodowski
Keyword(s):  
Random Walks ◽  
Random Field ◽  
Random Fields ◽  
Complete Convergence ◽  
Type Theorem ◽  
Random Variables ◽  
Necessary Condition ◽  
Dependent Random Variables ◽  
Negatively Dependent Random Variables ◽  
Convergence Results

Let  \(\{ X_{\bf n}, {\bf n}\in \mathbb{N}^d \}\) be a random field of negatively dependent  random variables.  The complete  convergence results for negatively dependent  random fields  are refined. To obtain the main theorem several lemmas  for convergence of families indexed by \(\mathbb{N}^d\)   have been proved. Auxiliary lemmas have wider application to study  the random walks on the lattice.

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