L r convergence for B-valued random elements

被引：8

作者：

Chen, Ping Yan ^{[1
]}

Wang, Ding Cheng ^{[2
]}

机构：

[1] Jinan Univ, Dept Math, Guangzhou 510630, Guangdong, Peoples R China

[2] Univ Elect Sci & Technol China, Sch Appl Math, Chengdu 610054, Peoples R China

来源：

ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2012年 / 28卷 / 04期

基金：

中国国家自然科学基金;

关键词：

L-r convergence; random element; Rademacher type p; Marcinkiewicz-Zygmund strong law of large number; P BANACH-SPACES; WEIGHTED SUMS; LARGE NUMBERS; UNIFORM INTEGRABILITY; WEAK LAW; THEOREMS;

D O I：

10.1007/s10114-011-9475-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The paper investigates L (p) convergence and Marcinkiewicz-Zygmund strong laws of large numbers for random elements in a Banach space under the condition that the Banach space is of Rademacher type p, 1 < p < 2. The paper also discusses L (r) convergence and L (r) bound for random elements without any geometric restriction condition on the Banach space.

引用

页码：857 / 868

页数：12

共 20 条

[11]

Gan S. X., 2001, WUHAN U J NATURAL SC, V7, P14

[12] LAW OF LARGE NUMBERS AND CENTRAL LIMIT-THEOREM IN BANACH-SPACES [J].

HOFFMANNJORGENSEN, J ;

PISIER, G .

ANNALS OF PROBABILITY, 1976, 4 (04) :587-599

[13] Convergence of randomly weighted sums of Banach space valued random elements and uniform integrability concerning the random weights [J].

Hu, TC ;

Cabrera, MO ;

Volodin, AI .

STATISTICS & PROBABILITY LETTERS, 2001, 51 (02) :155-164

[14]

Ledoux M., 1991, Probability in Banach Spaces

[15]

Mourier Edith, 1953, Annales de l'institut Henri Poincare, V13, P161

[16]

Pyke K., 1968, ANN MATH STAT, V32, P379

[17] Mean convergence theorems with or without random indices for randomly weighted sums of random elements in rademacher type p banach spaces [J].

Rosalsky, A ;

Sreehari, M ;

Volodin, AI .

STOCHASTIC ANALYSIS AND APPLICATIONS, 2003, 21 (05) :1169-1187

[18]

Thanh L. V., 2006, J APPL MATH STOCHAST, V16, P1

[19]

Wang X.C., 1992, NE MATH J, V8, P349

[20] SOME RESULTS ON THE CONVERGENCE OF WEIGHTED SUMS OF RANDOM ELEMENTS IN SEPARABLE BANACH-SPACES [J].

WANG, XC ;

RAO, MB .

STUDIA MATHEMATICA, 1987, 86 (02) :131-153

← 1 2 →