On the Kolmogorov inequalities for quadratic forms of dependent uniformly bounded random variables

Abstract

Some Kolmogorov probability inequalities for quadratic forms and weighted quadratic forms of negative superadditive dependent (NSD) uniformly bounded random variables are provided. Using these inequalities, some complete convergence of randomized quadratic forms under some suitable conditions are evaluated. Moreover, various examples are presented in which the given conditions of our results are satisfied.Kolmogorov inequality Negative superadditive dependent Quadratic forms Complete convergence