Abstract
Abstract : Strong laws of large numbers for a sequence x sub n of random functions in D(0,1) are derived using new pointwise conditions on the first absolute moments, which improve on known results. In particular, convex tightness is not implied by the hypotheses of the theorems. It is shown that convex tightness is is preserved when random functions are centered, and this result is applied to improve some known strong laws for weighted sums in D(0,1). A weak law of large numbers is proved using a new pointwise condition on the first moments and some weak laws for weighted sums are improved upon by weakening the hypotheses. A study is made of relationships among several conditions on X sub n which appear as hypotheses in laws of large numbers. (Author)
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.
