Best Possible Sufficient Conditions for Strong Law of Large Numbers for Multi-Indexed Orthogonal Random Elements

Kuo-Liang Su

International Journal of Mathematics and Mathematical Sciences, 2007, vol. 2007, 1-15

Abstract:

It will be shown and induced that the d -dimensional indices in the Banach spaces version conditions ∑ n ( E ‖ X n ‖ p / | n α | p ) < ∞ are sufficient to yield lim min 1 ≤ j ≤ d ( n j ) → ∞ ( 1 / | n α | ) ∑ k ≤ n ∏ j = 1 d ( 1 − ( k j − 1 ) / n j ) X k = 0 a.s. for arrays of James-type orthogonal random elements. Particularly, it will be shown also that there are the best possible sufficient conditions for multi-indexed independent real-valued random variables.

Date: 2007
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJMMS/2007/086909.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJMMS/2007/086909.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:086909

DOI: 10.1155/2007/86909

Access Statistics for this article

More articles in International Journal of Mathematics and Mathematical Sciences from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().