期刊論文
| 學年 | 66 |
|---|---|
| 學期 | 1 |
| 出版（發表）日期 | 1978-01-01 |
| 作品名稱 | Convergence of weighted sums of tight random elements |
| 作品名稱（其他語言） | |
| 著者 | Wei, Duan |
| 單位 | 淡江大學財務金融學系 |
| 出版者 | |
| 著錄名稱、卷期、頁數 | Journal of multivariate analysis 8(2), pp.282-294 |
| 摘要 | Convergence of weighted sums of tight random elements {Vn} (in a separable Banach space) which have zero expected values and uniformly bounded rth moments (r > 1) is obtained. In particular, if {ank} is a Toeplitz sequence of real numbers, then | Σk=1∞ ankf(Vk)| → 0 in probability for each continuous linear functional f if and only if ‖Σk=1∞ ankVk ‖→ 0 in probability. When the random elements are independent and max1≤k≤n | ank | = O(n−8) for some 0 < 1s < r − 1, then |Σk=1∞ ankVk ‖→ 0 with probability 1. These results yield laws of large numbers without assuming geometric conditions on the Banach space. Finally, these results can be extended to random elements in certain Fréchet spaces. |
| 關鍵字 | Random elements;weighted sums;tightness;symmetry;Schauder basis;convergence in probability and almost surely;laws of large numbers;Banach spaces and Fréchet spaces |
| 語言 | en |
| ISSN | |
| 期刊性質 | 國內 |
| 收錄於 | |
| 產學合作 | |
| 通訊作者 | |
| 審稿制度 | 否 |
| 國別 | TWN |
| 公開徵稿 | |
| 出版型式 | ,電子版 |
| 相關連結 |
機構典藏連結 ( http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/72351 ) |