Title : ( some maximal inequalities for quadratic forms of negative superadditive dependence r.v. s )
Authors: negar eghbal , Mohammad Amini , Abolghasem Bozorgnia ,
Full TextAbstract
Let {X_n; n geq1 }$ be a sequence of negative superadditive dependence random variables with E(X^2_n) < infty , for all n geq 1 . Denote $T_n = displaystyle sum_{1 leq i<j leq n} X_iX_j and Q_n = displaystyle sum_{1 leq i<j leq n} a_{ij}X_iX_j , where {a_{ij}; 1 leq i<j leq n } is an array of real numbers. We derive two maximal inequalities for quadratic forms $T_n$ and $Q_n$, then, using these inequalities we obtain strong law of large numbers and the rate of almost sure convergence under some suitable conditions on E(X^2_n)$ and {a_{ij}; 1 leq i<j leq n }
Keywords
, Quadratic forms, Negative superadditive dependence, Complete convergence
@inproceedings{paperid:1011506,
author = {Eghbal, Negar and Amini, Mohammad and Bozorgnia, Abolghasem},
title = {some maximal inequalities for quadratic forms of negative superadditive dependence r.v. s},
booktitle = {هفتمین سمینار احتمال و فرآیندهای تصادفی},
year = {2009},
location = {اصفهان, IRAN},
keywords = {Quadratic forms; Negative superadditive
dependence; Complete convergence},
}
%0 Conference Proceedings
%T some maximal inequalities for quadratic forms of negative superadditive dependence r.v. s
%A Eghbal, Negar
%A Amini, Mohammad
%A Bozorgnia, Abolghasem
%J هفتمین سمینار احتمال و فرآیندهای تصادفی
%D 2009
