Best Possible Sufficient Conditions for Strong Law of Large Numbers for Multi-Indexed Orthogonal Random Elements
It will be shown and induced that the d-dimensional indices in the Banach spaces version conditions ∑n(E‖Xn‖p/|nα|p)<∞ are sufficient to yield limmin1≤j≤d(nj)→∞(1/|nα|)∑k≤n∏j=1d(1−(kj−1)/nj)Xk=0 a.s. for arrays of James-type orthogonal random elements. Particularly, it will be shown also that the...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2007-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2007/86909 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | It will be shown and induced that the d-dimensional indices in the Banach spaces version conditions ∑n(E‖Xn‖p/|nα|p)<∞ are sufficient to yield limmin1≤j≤d(nj)→∞(1/|nα|)∑k≤n∏j=1d(1−(kj−1)/nj)Xk=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. |
|---|---|
| ISSN: | 0161-1712 1687-0425 |