教師資料查詢 | 類別: 期刊論文 | 教師: 韋伯韜 WEI, PO-TAO (瀏覽個人網頁)

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
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產學合作
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國別中華民國
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