The limit theorems of random elements in spaces of type p

• Main Authors: Chang, Hen-Chao, 張亨兆
• Other Authors: Tien-Chung Hu
• Format: Others
• Language: zh-TW
• Published: 1997
• Online Access: http://ndltd.ncl.edu.tw/handle/27628168932584654116

博士 === 國立清華大學 === 數學系 === 85 === We cosider some limit problems of random elements in this paper. In Chppter 1,we give the basic definitions and elementry properties of random elements. And we introduce a space of type p and the Levy''s inequalities in Banach spaces. In Chapter 2, we consider the necessary and sufficent conditions of complete convergence of arrayes of random elements. In Section 2.2, we obtain the sufficent condions of polynamial order. In Section 2.3, the necessary result is proved. In Section 2.4, we consider the general cases. In Chapter 3, we consider the almost sure convergence of weighted sums, using the Marcinkiewicz''s law of large numbers in a space of type p. In Section 3.2, we develop a tool-the Marcinkiewicz''s law of large numbers in a space of type p. In Section 3.3, we discuss the almost sure convergence of weighted sums of a sequence of random elements, and the weight is an array of random variables.