Some limit theorems for weighted sums of random variable fields期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Some limit theorems for weighted sums of random variable fields

Authors:	Gan Shixin Chen Pingyan

Affiliation:	(1) School of Mathematics and Statistics, Wuhan University, 430072 Wuhan Hubei, China;(2) Department of Mathematics, Jinan University, 510630 Guangzhou Guangdong, China

Abstract:	Let ${ X_{overline n } ,overline n in N^d }$ be a field of Banach space valued random variables, O<r<p≤2 and ${ a_{overline n ,overline k } ,(overline n ,overline k in N^d times N^d ,overline k leqslant overline n }$ a triangular array of real numbers, whereN ^d is thed-dimensional lattice (d≥1). Under the minimal condition that ${ \|\|X_{overline n } \|\|^r ,overline n in N^d }$ is ${ \|a_{overline n ,overline k } \|^r ,(overline n ,overline k )} in N^d times N^d ,overline k leqslant overline n }$ integrable, we show that $sumlimits_{_{overline k leqslant overline n } } {a_{overline n ,overline k } } X_{overline k } underrightarrow {{text{(or a}}{text{.s)}}}$ 0 as . In the above if 0<r<1, the random variables are not needed to be independent. If 1≤r<p≤2, and Banach space valued random variables are independent with mean zero we assume the Banach space is of typep. If 1≤r<p≤2 and Banach space valued random variables are not independent we assume the Banach space isp-smoothable. Foundation item: Supported by the National Natural Science Foundation of China(10071058) Biography: GAN Shixin(1939-), male, Professor, research direction martingale theory, probability limiting theory and Banach space geometry theory.

Keywords:	Banach space of type p multidimensional index strong law of large numbers Lr convergence weighted sums of random variable fields martingale difference array
本文献已被 CNKI 万方数据 SpringerLink 等数据库收录！

设为首页 | 免责声明 | 关于勤云 | 加入收藏