# Some mean convergence and complete convergence theorems for sequences of $m$-linearly negative quadrant dependent random variables

Yongfeng Wu; Andrew Rosalsky; Andrei Volodin

Applications of Mathematics (2013)

- Volume: 58, Issue: 5, page 511-529
- ISSN: 0862-7940

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topWu, Yongfeng, Rosalsky, Andrew, and Volodin, Andrei. "Some mean convergence and complete convergence theorems for sequences of $m$-linearly negative quadrant dependent random variables." Applications of Mathematics 58.5 (2013): 511-529. <http://eudml.org/doc/260633>.

@article{Wu2013,

abstract = {The structure of linearly negative quadrant dependent random variables is extended by introducing the structure of $m$-linearly negative quadrant dependent random variables ($m=1,2,\dots $). For a sequence of $m$-linearly negative quadrant dependent random variables $\lbrace X_n, n\ge 1\rbrace $ and $1<p<2$ (resp. $1\le p <2$), conditions are provided under which $n^\{-1/p\} \sum _\{k=1\}^\{n\} (X_k - EX_k) \rightarrow 0$ in $L^1$ (resp. in $L^p$). Moreover, for $1\le p < 2$, conditions are provided under which $n^\{-1/p\} \sum _\{k=1\}^\{n\} (X_k - EX_k)$ converges completely to $0$. The current work extends some results of Pyke and Root (1968) and it extends and improves some results of Wu, Wang, and Wu (2006). An open problem is posed.},

author = {Wu, Yongfeng, Rosalsky, Andrew, Volodin, Andrei},

journal = {Applications of Mathematics},

keywords = {$m$-linearly negative quadrant dependence; mean convergence; complete convergence; -linearly negative quadrant dependence; -convergence; complete convergence},

language = {eng},

number = {5},

pages = {511-529},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Some mean convergence and complete convergence theorems for sequences of $m$-linearly negative quadrant dependent random variables},

url = {http://eudml.org/doc/260633},

volume = {58},

year = {2013},

}

TY - JOUR

AU - Wu, Yongfeng

AU - Rosalsky, Andrew

AU - Volodin, Andrei

TI - Some mean convergence and complete convergence theorems for sequences of $m$-linearly negative quadrant dependent random variables

JO - Applications of Mathematics

PY - 2013

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 58

IS - 5

SP - 511

EP - 529

AB - The structure of linearly negative quadrant dependent random variables is extended by introducing the structure of $m$-linearly negative quadrant dependent random variables ($m=1,2,\dots $). For a sequence of $m$-linearly negative quadrant dependent random variables $\lbrace X_n, n\ge 1\rbrace $ and $1<p<2$ (resp. $1\le p <2$), conditions are provided under which $n^{-1/p} \sum _{k=1}^{n} (X_k - EX_k) \rightarrow 0$ in $L^1$ (resp. in $L^p$). Moreover, for $1\le p < 2$, conditions are provided under which $n^{-1/p} \sum _{k=1}^{n} (X_k - EX_k)$ converges completely to $0$. The current work extends some results of Pyke and Root (1968) and it extends and improves some results of Wu, Wang, and Wu (2006). An open problem is posed.

LA - eng

KW - $m$-linearly negative quadrant dependence; mean convergence; complete convergence; -linearly negative quadrant dependence; -convergence; complete convergence

UR - http://eudml.org/doc/260633

ER -

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