- 學位論文
關於巴拿赫空間隨機數列的完全收斂之研究
A Study on complete convergence for stochastic arrays taking values in Banach space
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摘要
巴拿赫空間隨機變數是歐式空間隨機變數的推廣, 這篇文章主 要是討論巴拿赫空間隨機變數的完全收斂,且介紹一些巴拿赫空間隨 機變數的性質. Kruglov, Volodin and Hu 在2006年發表了一系列有關歐氏空間隨機 變數數列完全收斂的文章, 我們將上述結果推廣至巴拿赫空間隨機 變數的完全收斂.
關鍵字
完全收斂並列摘要
A complete convergence theorem for arrays of rowwise independent random variables was proved by Kruglov, Volodin, and Hu [12]. In this note, we discuss some recent on complete convergence for arrays of rowwise independent Banach space valued random elements.
並列關鍵字
random element參考文獻
[1] B.J. Pettis, 1938. On integration in vector spaces, Trans. Amer. Soc. 44, 277-304.
[2] J. Hoffmann-Jørgensen, 1974. Sums of independent Banach space valued random variables. Studia Mayh. LII, 159-186.
[3] J. Hoffmann-Jørgensen, G. Pisier, 1976. The law of large numbers and the central limit theorem in Banach spaces, Ann. Probab. 4, 587-599.
[5] P. Erdős, 1949. On a theorem of Hsu and Robbins, Ann. Math. Statist. 20, 286-291.
[6] P.E. Kopp, 1984. Martingales and stochastic integrals, New York-London.