Abstract
Abstract In this paper, we study the strong law of large numbers for a class of random variables satisfying the maximal moment inequality with exponent 2. Our results embrace the Kolmogorov strong law of large numbers and the Marcinkiewicz strong law of large numbers for this class of random variables. In addition, strong growth rate for weighted sums of this class of random variables is presented. MSC:60F15.
Highlights
Let {Xn, n ≥ } be a sequence of random variables defined on a fixed probability space
Let {an, n ≥ } and {bn, n ≥ } be sequences of positive numbers, an bn represents that there exists a constant C > such that an ≤ Cbn for all n
2 Preliminaries The following lemmas and definition will be needed in this paper
Summary
Let {Xn, n ≥ } be a sequence of random variables defined on a fixed probability space ( , F , P). Under a pairwise independent assumption, Rosalsky [ ] obtained some SLLNs for weighted sums of pairwise independent and identically distributed random variables. ) if {Xn, n ≥ } is a sequence of pairwise independent random variables satisfying presented the following result: (Sung [ ]) A random variable sequence {Xn, n ≥ } is said to satisfy the maximal moment inequality with exponent if for all n ≥ m ≥ , there exists a constant C independent of n and m such that k
Sign-in/Register to view highlights & summary 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.
