期刊論文

標題 Convergence of weighted sums of tight random elements
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 英文
ISSN
期刊性質 國內
收錄於
產學合作
通訊作者
審稿制度
國別 中華民國
公開徵稿
出版型式 ,電子版