Some maximal inequalities for quadratic forms of negative superadditive dependence random variables

In this paper, we derive two maximal inequalities for quadratic forms of negative superadditive dependence random variables. Then, we obtain the strong law of large numbers and the rate of convergence under some suitable conditions on existence of moment. Noting that, the dependence structure that has been studied is an extension of negative association and sometimes more useful than it and can be used to get many important probability inequalities.