数学物理学报(英文版) ›› 2009, Vol. 29 ›› Issue (2): 305-312.doi: 10.1016/S0252-9602(09)60031-X

• 论文 • 上一篇    下一篇

GENERALIZED ROSENTHAL’S INEQUALITY FOR BANACH-SPACE-VALUED MARTINGALES

于林   

  1. College of Sciences, China Three Gorges University, Yichang 443002, China
  • 收稿日期:2007-08-05 出版日期:2009-03-20 发布日期:2009-03-20
  • 基金资助:

    Supported by the Scientific Research Foundation of Hubei Province (D200613001) and the National Natural Science Foundation of China (10371093)

GENERALIZED ROSENTHAL’S INEQUALITY FOR BANACH-SPACE-VALUED MARTINGALES

Yu Lin   

  1. College of Sciences, China Three Gorges University, Yichang 443002, China
  • Received:2007-08-05 Online:2009-03-20 Published:2009-03-20
  • Supported by:

    Supported by the Scientific Research Foundation of Hubei Province (D200613001) and the National Natural Science Foundation of China (10371093)

摘要:

A generalized Rosenthal’s inequality for Banach-space-valued martingales is proved, which extends the corresponding results in the previous literatures and character-izes the p-uniform smoothness and q-uniform convexity of the underlying Banach space. As an application of this inequality, the strong law of large numbers for Banach-space-valued martingales is also given.

关键词: Rosenthal’s inequality,  Φ-inequality, martingales, p-uniform smoothness, q- uniform convexity

Abstract:

A generalized Rosenthal’s inequality for Banach-space-valued martingales is proved, which extends the corresponding results in the previous literatures and character-izes the p-uniform smoothness and q-uniform convexity of the underlying Banach space. As an application of this inequality, the strong law of large numbers for Banach-space-valued martingales is also given.

Key words: Rosenthal’s inequality,  Φ-inequality, martingales, p-uniform smoothness, q- uniform convexity

中图分类号: 

  • 60G42