Abstract
In [3], we began a study of convergence of quadratic forms in independent random variables. Simultaneously, Fau Dyk Tin and G. E. Silov [2] initiated their study of this problem but restricted to the case of quadratic mean convergence and normal variables. Our aim in this paper is to consider carefully the problem of almost sure convergence (convergence with probability one). Several of our results will generalize well known theorems for series of independent random variables. We shall assume throughout that X1, X2, *** is a sequence of independent real random variables with E(Xk) = 0 and E(Xk2) = 1, k = 1, 2, * .. . Note that we do not assume that the Xk's are identically distributed or place conditions on the higher moments. Let (aJk), j, k = 1, 2, ***, be a real (not necessarily symmetric) matrix and let
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
